Genetic engineering (GM) is very recent

"I can also add something to that. I heard that the problem with grains is that decades ago, a certain amount of them have been genetically engineered to resist insects. I don't need to say more."

Genetic engineering (GM) is a term that is much too loosely used by many.  In reality, it is the modification of DNA of a plant or animal by the introduction of the DNA from a different species.  A plant can have the DNA of an animal introduced into it and vica versa.  This has been going on for little more than ten years, not decades.  GM technology as it relates to plants has been around for not much more than 20 years.  Almost all modification of plants prior to GM was via hybridization, which is a simply selective breeding.  If you read Mercola's referenced site, this is what it says regarding cereal grains:

From Mercola:

"Generally, in most parts of the world, whenever cereal-based diets were first adopted as a staple food replacing the primarily animal-based diets of hunter-gatherers, there was a characteristic reduction in stature, a reduction in life span, an increase in infant mortality, an increased incidence of infectious disease, an increase in diseases of nutritional deficiencies (i.e., iron deficiency, pellagra), and an increase in the number of dental caries and enamel defects."

So the increase in disease, reduction of life span, and on and on began with the advent of agriculture which occurred about 10,000 years ago.  Trying to blame our ills on GM is downright foolishness.  It is and has been the introduction of cereal grains, exacerbated by the more recent advent of polished (white) rice and white flour.

We have hybridized fruits and vegetables so significantly that many can't even be found in nature.  Go find a wild green bean.  Or a wild pumpkin, and many others.  It is exactly what early humans did with the advent of agriculture.  They learned hybridization very early with both plants and animals and a great deal of what we eat - besides cereal grains, bear little resemblance to what our hunter gatherer ancestors ate, just as most dogs bear little resemblance to wolves from which all of them are descended.  (All domestic dogs are descended from wolves which is hybridization and not GM.)