Where the rule came from
The idea that plant proteins are incomplete, and must be carefully paired at every meal, spread from a popular 1971 book and stuck. It sounds scientific, and it is half true: individual plant foods do have different amino acid profiles. The part that did not hold up is the meal-timing rule.
What the dietitians actually say
The Academy of Nutrition and Dietetics, the professional body for US dietitians, addressed this directly in its position paper on vegetarian diets.
Primary source 01 / 02
The terms complete and incomplete are misleading in relation to plant protein. Protein from a variety of plant foods, eaten during the course of a day, supplies enough of all indispensable (essential) amino acids when caloric requirements are met.
In other words, your body pools amino acids from everything you eat across the day, so the beans at lunch and the bread at dinner combine on their own. The practical advice is simpler than the myth:
Primary source 02 / 02
The regular use of legumes and soy products will ensure an adequate protein intake for the vegetarian, as well as providing other essential nutrients.
Eat a normal, varied plant diet with enough calories, lean on legumes and soy, and the protein takes care of itself. The one group that can fall short is people eating too little food overall, or a very restricted diet like fruitarianism, where the problem is calories, not amino acid maths.