I'm sorry, that's just not true. You don't need them in any sort of balance. All whole foods (even plants) have more than enough of each, if you eat enough calories.
The "balance" that is spoken of is in comparison to the amino acid profile found in meat. It was assumed that this was the proper balance. That is a fallacious argument. It would be comparable to looking at an orange and deciding that an orange has the proper balance of vitamins and minerals, and should therefore combine foods to make sure they have the nutrient profile of an orange. The truth is that if you get more than the minimum amount of each amino acid then you are fine. A full days calories worth of any
whole food on earth (except gelatin) will have more than the minimums of each. The exception being some fruits, which is easily made up for by eating the highest protien food on earth, greens.
Here is a write up of the retraction made by the very person who introduced it in the first place.
Quote:
The protein combining theory was based on interpretation of studies performed in the early 1900s on the growth of rats. The theory entered popular consciousness with the publication of Frances Moore Lappé's 1971 bestseller Diet for a Small Planet. In later editions of Diet for a Small Planet, beginning in 1981, Lappé changed her position on protein combining. In this later edition, Lappé wrote:
"In 1971 I stressed protein complementarity because I assumed that the only way to get enough protein ... was to create a protein as usable by the body as animal protein. In combating the myth that meat is the only way to get high-quality protein, I reinforced another myth. I gave the impression that in order to get enough protein without meat, considerable care was needed in choosing foods. Actually, it is much easier than I thought.
"With three important exceptions, there is little danger of protein deficiency in a plant food diet. The exceptions are diets very heavily dependent on [1] fruit or on [2] some tubers, such as sweet potatoes or cassava, or on [3] junk food (refined flours, sugars, and fat). Fortunately, relatively few people in the world try to survive on diets in which these foods are virtually the sole source of calories. In all other diets, if people are getting enough calories, they are virtually certain of getting enough protein."[3]
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And to clarify Okinawans traditionally eat a diet based on sweet potato (about 70% of calories) and don't have problems getting protien form veggies.