This is incorrect. What, pray tell, is a "complete protein?" There are no amino acids in animals that are not found in plants. You appear to be wholly misinformed on this subject.
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.
You don't need to eat meat to get your protein.
So protein quality and quantity can't likely be insured by eating any old vegetables. Its not as simple as 'don't eat meat'.