Mailbox was nice, but I dropped it after a week when your point occurred to me. As far as I could tell, the only reason it needed full access was for push notifications. There was no discussion at all of account security, and I just couldn't bring myself to trust them. There's no way one of the usual cutesy startup apologies would cut it here if they compromised my email.

I'm back to Sparrow now (which doesn't do push) and quite happy: Mail.app tells me I have a new message, then I process my emails in Sparrow.