It's easy: "We'll get you X thousand customers, you drop the fees". Banks do special arrangements like this all the time.
So in actuality, they will charge you whatever the bank your money is currently in charges them.
As for drawing a negative balance, I don't think the bank your money is in will charge BankSimple, because I don't think BankSimple would open up thousands of individual accounts for each customer. The easier way to do it would be to have a single 'slush' account where all of the money goes. In that case, BankSimple wouldn't be charged for your overdraft, because their account never actually goes under.
So clearly BankSimple has worked this out with the underlying institution to create individual accounts for you. That seems like it has to be true, the only other alternative would be some deal cut with the FDIC which is not probable IMO.
But I think the original guy in this thread is wrong, too, because what BS can do, despite you having an individual account in your name at their backend provider, is ensure on your behalf that said account never goes negative. That is, abstract overdrafts within their Tier by extending you a line of credit -- deposited into your backend account. This is exactly what they're doing if I understand correctly.
Not to mention, if you're BankSimple and you go to Chase and you say "What kind of deal can you give us on APY and fees? I can bring you 900,000 accounts with $4.5Bn in deposits to your bank?"
Banks start fawning over you once you have $20k in an account with them. If you're ever fortunate enough to have $100k you start to get serious banking attention. $4.5 billion dollars is an enormous amount of capitalization -- even for huge banks like BofA and JPMC.