There are actually three major players in the transaction aggregation space: Intuit, Yodlee, and Plaid. We use Plaid, but it works the same as Intuit. In fact, Plaid has a partnership with Intuit to backfill support for bank accounts.
We never store any credentials on our system, and our access is read only. I can go on for days about why I think our system is more secure than, say, Chase[0], but if you trust Mint's practices it's probably sufficient to say that we use an almost identical system.
[0] https://en.wikipedia.org/wiki/2014_JPMorgan_Chase_data_breac...