You're right about combining beans (lentils) and rice to make a complete protein. The problem is with protein and high-carb/starches...like the standard meat and potatoes. Protein and low-carbs...like fish and salad...are fine. Some people don't have as much problem with the protein/starch combo, but others don't digest them so well and get a lot of gas.
Milk, poultry, fish, eggs, milk and cheese are considered complete proteins containing all eight essential amino acids. Nuts and legumes are incomplete proteins.