"A complete protein (or whole protein) is a source of protein that contains an adequate proportion of all nine of the essential amino acids necessary for the dietary needs of humans or other animals"

http://en.wikipedia.org/wiki/Complete_protein

Many plants have "complete" amino acid profiles but one or more amino acids are too low to be completely adequate for humans. In this case, another protein source with a supplemental amino acid profile is required in order to balance out the deficiency in the first.

Quoting from your own source: >Nearly all foods contain all twenty amino acids in some quantity, and nearly all of them contain the essential amino acids in sufficient quantity.

You don't need to eat meat to get your protein.

But traditional foods in America included beans, corn, squash. Presumably to get a reliable source of protein. The natives weren't dieticians; they ate that because villages with that tradition thrived.

So protein quality and quantity can't likely be insured by eating any old vegetables. Its not as simple as 'don't eat meat'.