While I think everyone agrees that your application looks strong on paper, the only things that are likely off are letters of rec and statement of purpose.
(Disclaimer: Not on any committees or anything, just a fellow grad student)
1) Letters. Sending 6 (or generally, more than about 3-4) seems to suggest you don't have confidence in any subset of them, and are generally trying to just blanket the admissions committee with information. More is not better. From what it sounds like, it's also likely that none of them were really stellar ("Got an A in my class" isn't good enough).
2) Statement. It seems you might not have been specific enough. Tons and tons of students apply to Hep-th saying they want to do string theory because it's sexy and they want to unify gravity with quantum mechanics and become the next Einstein. Hyperbole aside, simply stating an interest in hep-th is worrying because it shows you don't really know what working in the field is like. I realize this isn't completely true given your case, given that you've taken some relevant undergrad courses, but nevertheless its your statement which really tells this. Wording can be everything, and having confidence in your abilities/ambitions seems more important than making excuses for a less-than-perfect GPA. If your statement is a consistent string of trying to 'fill in gaps' in your academic transcript, it's likely worth less than a cohesive, strong statement about your research interests and where you'd fit in at the institution.
Finally, just remember that these places are extraordinarily competitive. Many applicants you're competing against have already studied hep-th for a year or so. So, statistical fluctuations do happen when you're competing against such a pool of candidates.