Unfortunately, there is a reason why getting a merchant account is a pain in the ass. The bank doesn't want the risk (for good reason).
The thing about Square isn't the device... it's the service. So when things go poorly, they will be the ones that have to foot the bill. If they open things up too widely, then they will be exposing themselves to huge risk.
From the video on the square site it seemed like person to person transactions are encouraged. I'm guessing turn around time for money transfers are going to be longer and maybe a secondary online approval process for some transactions for non-merchant accounts.