The tomato having more lycopene is deliberate misleading.
This is all based on Tomato processing Industry based research.
In a bid to promote people to use tomato paste and other processed tomato products, "the Industry" came up with devious research.
They basically went by weight.
They took 100 grams of tomato paste and 100 grams of tomatoes and compared the lycopene levels.
What is wrong is that if you ever use tomato paste you will know that around 2-3 spoons are equal to 1 tomato(it varies based on the thickness of the paste).
So 100 grams of tomato paste could actually be equal to maybe half a kg of tomatoes.

So this lies has been spread by the media, if doctors and nutritionist believe this is only because they have got the news from the media(which obviously lives of advertising of these tomato processing companies).

Also the above research was not a "Raw Vs cooked tomato" research. It was a "whole cooked tomatoes Vs processed tomatoes research".
The concept of raw food was almost non-existant when this research was conducted. The research is also very old(it was conducted and promoted during the time Tomato paste was introduced in the market). The companies were trying prove that their tomato paste was not only convenient that whole tomatoes but also having more lycopene(means more healthy)
The anti-raw brigade and the trolls are purposefully "assuming" that whole tomatoes is equal to raw tomatoes, just to argue their point.

There was a recent study that boiled carrots had more beta carotene and anti-oxidants than raw carrots.

Here too when I finally got my hands on the research papers.
Again this research was never conducted as a Raw vs cooked carrot research.
Carrots were taken boiled and then pureed into a fine paste. Then it was kept under 40 degrees Celsius temperature for 15 days(or more).
Then whatever was left was compared with the exact same weight of raw carrots. Obviously they found more nutrients.
Let me explain how.
If you see the carrots were purreed. We all know that juiced carrots allow better assimilation of nutrients.
Then it was kept for 15 days under conditions similar to dehydrations.
Which means the carrots puree lost all water. Thus reducing its weight and actually making it a sort of "concentrate"
So you can say if they started off with 500 grams carrots they would be left with 100 grams of dehydrated pureed carrot pulp.
They simply take this "concentrate" carrot pulp and compare it with 100 grams of raw full carrots. Which is wrong.

I think anyone with a little bit of common sense can predict that if the same carrots were only pureed and dehydrated(NOT BOILED) it would had more nutrient content than Raw whole carrots.

You can that there is a deliberate attempt to "scare" people of raw foods.
These are just two vegetables among the different species of vegetables available.
It is just two nutrients in question.
If you check you will see that Watermelon contains more lycopene than tomatoes.
Also once can easily attain a healthy dose of beta carotene with just a few carrots. Cooking carrots may give you extra beta carotene which your body may not even use, but you end up losing the other benefits of carrots(like parasite cleansing effect).

What is preposterous that only these two vegetables are used to "declare" ALL raw foods as "less assimilated" when it is wrong. In comparison other raw foods have almost 100times benefits that its cooked versions.

Also if you have read recent CSPI list of "unsafe things to eat" they have included green leafy vegetables in it.
Just because it has been contaminated by e.coli.
The contamination could be by a person handling the ecoli who has not washed his hands(or maintained proper hygiene while tranporting the greens).
But CSPI has Blamed the veggies and not the fact that supermarkets should check its hygiene standards.
Supermarkets are ridden with cockroaches and you should know that they are the connectiong with such kind of bacteria that is only found in sewage and feces.

The same way another attempt to scare people off raw food is made by saying that it could be contaminate and unclean.
This maybe true in many cases but the solution is not to stay away, but rather to use Hydrogen peroxide, ozone or both to clean the veggies.
Here in India we soak veggies in thick solution of salt water(which kills all germs). Cauliflower is soaked in turmeric.
Free range Country(wild) chicken is never washed. They just de feather it and just roast it over the fire. Then they rub Turmeric powder on it and keep it for half an hour.
In the west they cannot even think of it.
There are enough of organic veggie washes too that can remove all germs from veggies(not pesticides, that can be solved by going for organic vegetables).

So this is all myth.
The problem with deficiencies in people who go raw is a perinnial problem with the west.
Like I love to say "they reinvent the wheel and get it wrong". Then they try to "westernize" it.
Ayurveda has prescribed raw diet ages ago. It is still used by many to cure disease like cancer(it takes only 18 days to cure diabetes and cancer, with the help of pranayama and detox treatment called panchakarma)
Ayurveda calls to eat the vegetables as fresh and soon as it is cut.
Once veggies are chopped they start to lose their nutrient when exposed to air.
But Many raw foodist do recipies which ask to dehydrate cut up vegetable for upto 12 hours!!!.
Also they have no knowledge of vegetables.
Instead of spending time making a burger out of flax seed. If they just spent time trying to make a tasty salad from all the vegetables they can put it. There will be no deficiencies.
I am on raw food.
I only eat salads. No exotic recipes.
To the west salads would mean only watercress, lettuce and if they get bold they go in for kale etc.
I just put in spinach, Mint leaves, Clilantro, Fenugreek leaves, Brahmi(and 5 other leaves that are locally available do not know the english names) lettuce, broccolli, cauliflower, Okhra, carrot, Bitter gourd, Ash gourd, Okhra, cabbage, beetroot, Kohlrabi, Mung bean sprouts, Raw turmeric(3 types)grated, pepper, black salt, lime. Raw olive oil or coconut oil.
Sometimes I splutter some mustard in coconut oil,(never use olive oil for cooking) and add is some red dried chillies, Curry leaves and cumin seeds, and then just let it cool a little and use it as a dressing in my salad. Then I add two tablespoons of raw coconut oil(to get the health benefits of raw coconut oil).
But the raw food fanatics do not want to cook anything. Just cooking a little oil for taste and adding just minute quantities of cooked spices(that too just spluttered) is not going to turn your raw food "useless".
I found it hard to believe that Victoria Boutenko after 9 years of going raw discovered that they were not eating Greens and that was the cause of their deficiency.
How can some one on a raw vegetable diet not know they have to consume greens!!!
Also raw foodist get very less protiens, because they do not know about sprouts and rarely use them.
Also I do not recomend a 100% raw diet, But a 99.9%. I think it would only help to include some good hot soups to which ginger, garlic can be added. Like quinoa soup.
Also one can cook the dressing in herbs and spices just for taste(that going through proccess of trying to make food look like junk food and also dehydrating it to make it eatable).
Brinjal/eggplants are not supposed to be eaten(Monkey do not eat them).
But raw foodist actually spend time dehydrating it and make raw vegan Eggplant parmesan.
Obviously they are going to get deficiencies.
Also brahmi and spirulina should be included in diet. because brahmi contains cobalt and precursor to B12. Thus giving a good source of B12.
Now B12 is another issue but after doing enough research I can confidently conclude that one get the required amount of B12 on a vegan veg diet. I would discuss that some other time.
Go raw and explore everything you can eat raw.
Also fruits are healthy. The sugars are not refined sugars.
When I switched to organic brown Sugar you could feel that the organic unprocessed Sugar is not acidic like refined sugar.
You just take refined Sugar and swirl it in your mouth you can feel some kind of reaction or "stress" or sensitivity on your teeth. you cannot but a finger on that feeling but it feels like acidic.
But you take unproccesed brown sugar and you do not feel the same. Infact you take organic palm jaggery and it feel great.
The same way sugars in fruits is not refined.
It is an entire package. So you can safe eat it and it will not affect the teeth.
The same way fruits contain methanol but it does not affect us.
Also a research found that there is an enzyme in fruits(name starting with S) that does not allow the sugars to "trigger" the kind of response it gives when you consume refined sugar.