It's not that I particularly trust mint, I just have seen my fair share of "identity theft" in my previous jobs and in my personal experience, and I've never seen anyone have issues due to a site like mint. Of the perhaps 50 cases of identity theft-type situations I've seen, all were either:
1) weird credit card charges that the credit card company caught right away and refunded; or
2) sadly, a family member who is in a bad financial place using a loved one's SSN to apply for utilities, credit cards, etc.
3) one case where a criminal was arrested, gave someone else's social, and then was later wanted by the feds, so they ended up putting out a warrant for the wrong person.
That's it, 100% of what I've seen. I doubt those one-time credit card charges came from mint, but even if they did, I've never seen a case where the credit card company didn't deal with it and refund it right away. The really bad ones are the family members, because it's harder to catch, usually ends up on your credit report, and the only way to really deal with it is to report your mother (yes, it's usually their mother) to the police.