It is easy to understand why many would believe this is the case. Below is a list of food ranked by the PDCAAS (protein digestibility corrected amino acid score), which is the measure of protein quality used by the World Health Organization. The list comes from Wikipedia.
1-1.21 cow's milk
1 casein (milk protein)
1 soy protein
1 whey (milk protein)
0.87 Sacha Inchi Powder
0.82 pea protein isolate
0.78 chickpeas and soybeans
0.75 black beans
Any food with a PDCAAS of 1.0 is a "perfect protein." In 1990, the FAO/WHO decided that "proteins having values higher than 1.0 would be rounded or 'leveled down' to 1.0 as scores above 1.0 are considered to indicate the protein contains essential amino acids in excess of the human requirements."
As you can see on the list, there are plenty of vegan options on that list that are equivalent to animal products. For example, rather than eat beef (0.92) you can eat soy (0.91). Rather than drink whey protein (1.0), you can drink soy protein (1.0).
However, someone eating, say, black beans, may believe that he would become protein deficient because black beans have a PDCAAS of 0.75.
However, people generally don't eat the same food all the time. A key limitation of the PDCAAS is that it doesn't take into consideration the fact that if you eat two or more foods with low PDCAAS, the combination of these foods can create a perfect PDCAAS of 1.0.
This concept is explained in the article: "[G]rain protein has a PDCAAS of about 0.4 to 0.5, limited by lysine. On the other hand, it contains more than enough methionine. White bean protein (and that of many other pulses) has a PDCAAS of 0.6 to 0.7, limited by methionine, and contains more than enough lysine. When both are eaten in roughly equal quantities in a diet, the PDCAAS of the combined constituent is 1.0, because each constituent's protein is complemented by the other."
Should we worry about protein deficiency? Is anyone protein deficient?
The video below by Dr Michael Gregor shows that statistically speaking, 97% of Americans are deficient in fiber whereas only 3% of Americans are deficient in protein. For the average person, getting enough fiber is far more of a concern than getting enough protein. Just about everyone gets more than enough protein.