It is also a bit out of place to, on one hand, say one does not care about labels, and then
(1) discriminate on the basis of labels (notably endorsing different sets of rights for mixed-sex and same-sex couples).
(2) campaign on being an American.
#2 isn't particularly serious, since people are often under the gun to provide sound bites, and it is a lesser of evils when it comes to labels. #1, though, is significantly harder to accept -- but it is still less egregious than the usual rhetoric of most Republicans saying they want "small government" and then trying to institute a strong "religious" code of morality (while she has done a "lite" version of the latter, I have not otherwise listened/read enough to see if she has tried to pass off the former).