Sparrow doesn't push because the app developer felt that they could not handle push, not because iOS doesn't allow them to. Considering Facebook messenger starts almost instantaneously, I'm still failing to see the practical benefit of android's form of multitasking.
AGAIN! You're completely ignoring my post and the blog.
They don't want to use push. It's expensive, inelegant and has security problems.
We've already covered that the push notification model adds unnecessary unreliability and overhead into the mix.
Apple recognised that and added the VOIP API. If you think about it, if Push Notifications were timely enough, you wouldn't need a VOIP API (or at least the part that listens for incoming calls).
From the link it says Apple won't allow it in the app store. But they also say iOS can do it if Apple allowed it...
They are talking about using one of the APIs (like VOIP or Location) to trick iOS into thinking that the App should be able to check for messages in the background.
i.e. they would pretend to be a VOIP App like Skype, listening for incoming calls - although they would actually be listening for new email.
As the App Store Guidelines state, Apps that misuse the Background APIs will be rejected, so that's a non-starter.