At least at one point, Mint used a information-clearinghouse by Yodlee that (by my understanding) did not require indefinite storage of actual login credentials for continued service, at least not for all target banks. Instead, after initial authorization, Mint held its own persistent delegated read-only credentials -- but not full read/write and login capabilities. This was essentially like the OAuth-style solution this author advocates (though using a system, Yodlee, that long predates OAuth itself).

I could be wrong about any of this, but I believe this was what allowed Mint to say, among other things, that they could provide your financial information without even knowing your name, and that no possible compromise of their servers could result in bank transfers.

Mint's current privacy info is insufficiently detailed to know if they still use this approach. They say "your bank login credentials are encrypted", suggestive that they retain 'login' abilities, but that might be a simplification or fallback (when the read-only delegation is unavailable).

Unfortunately, describing security in more detail often confuses and unnerves customers more than just saying the magic words that make people feel safe. So most companies, whether they are good or bad at security, oversimplify in their descriptions. (That is: the public descriptions that are most true and useful to knowledgeable users won't win an A/B test, maximizing either conversions or feelings of trust, with most customers.)

Update: Here's an old thread where I had questions, and a link provided by timf contributed to my understanding above: http://news.ycombinator.com/item?id=412715