If they didn't have push access and servers, how would they let you know when you had new mail? Third party iOS apps can't poll for new mail, so remote notifications are the only way!
+1. Push notification is the only way to notify about new emails. The trade-off is that you are gonna have to store user credentials on server. That's the reason why Sparrow didn't implement push notification.
Looks good. So you can store oauth on server, which should be safer. Is it possible for an oauth client to "suicide" on its permission? I'm thinking, in case a third-party service is comprised, they can just ask the oauth server to abandon their permission to avoid further loss for users.
Thats fine, when you get several hundred emails a day you don't want push notifications. If its important it shouldn't be going to me via email, I mean thats why I have a phone.