To expand on strongm's post (seems old habits die hard):
"Grammar" is defined as "The whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics." Of these, "syntax" is defined as "the arrangement of words and phrases to create well-formed sentences in a language." Finally, "punctuation" is defined as "the marks, such as period, comma, and parentheses, used in writing to separate sentences and their elements and to clarify meaning."
While one may perhaps argue from these definitions that punctuation is not a part of syntax, since punctuation marks are not themselves "words and phrases", I believe one may more convincingly argue that they are nevertheless part of "the arrangement of words and phrases to create well-formed sentences." Therefore, I am of the opinion that punctuation is a sub-category of syntax, which is itself a sub-category of grammar.
A bit of googling reveals that most online "Grammar" references include a section on punctuation, suggesting that my opinion is that of the majority. I did find one blog entry
here opining thus:
GRAMMAR refers to the way words are put together to make units of meaning...PUNCTUATION refers to the “symbols” we use to help people read/process sentences the way we want them to be heard and understood.
But I only found the one, and the poster doesn't style herself as an authority on either grammar or punctuation.
Thus, in my opinion, the "grammar vigilante" was entirely correct to so style himself. Styling himself a "punctuation vigilante" (or dare I say "apostrophe vigilante") would be correct as well, if he wanted to limit his practice to the eradication of the "apostrophosis" epidemic and other punctuation-related diseases. But that would be more confining to any future aspirations he might have to expand his vigilanteism to address other grammar-related diseases.
An unforeseen consequence of the information revolution has been the exponential propagation of human error.