If the comment is purely a "thank you," then it's probably not necessary....but no reason to flag as "too chatty," in my opinion, because (as you quoted from animuson), it is certainly nice to reinforce the idea that the people who help you (and whom you help) are human, which is something that I've noticed that some people forget or lose sight of on occasion. [ Once I saw a user's profile (don't remember which) that simply wrote "I am a human being, not a human resource" ]
All the same, you might want to refrain from making these kinds of comments, all the same, just because if everyone did it, there would be no room for regular comments that critique posts and request more information.
However, even if you would flag a simple "Thanks! [15 char]" comment as "too chatty," there is another type of thank you comment. When the comment contains a nice compliment, like "Thanks for this well-researched and well-written answer," or "Thanks for the speedy answer," then I think that it should definitely be left alone, as it is something that really says something nice about the answerer (and the complimenter), and could be of lasting value.
Those comments, if you feel like making them, certainly should be made, as a show of appreciation for an outstanding (quick, well-written, well-researched etc) post. I, for one, really appreciate when someone goes out of their way to say something nice about my posts, and hope that others appreciate it when I compliment their posts.