Ok, interesting. Very interesting for the advertisement this is doing but on the fact that you don't need an intermediary ... how is blockchain.info not an intermediary? Yes, with bitcoin, you can run your own top level (in the sense that there is no higher authority) piece of banking infrastructure on your phone as you can both run a full client (schildbach) and even mine on mobile devices (although I don't know if phones reach kH/s) but this is not what this app does. Welcome, blockchain.info is your bank.
Blockchain.info is an intermediary but the User is not dependant on it. You remain the only person who can access your wallet and as long as you keep a backup are free to move your keys to a different client at anytime.
It's a centralised interface for convenience with the ability to fall back to the decentralised network if need be.
Ok, you have a JS wallet that does not send you the priv keys. For the iPhone client do you also not have access to the private keys?? If so, I apologize for my quick reply.
I already knew you are very flexible exporting and importing keys (although I don't understand why I would want to export keys from an online service as moving away would also mean not to use secrets I shared with the entity I'm leaving) but I thought the only full-blown mobile client was the Schildbach client for Android and that has its limitations when it comes to poor connectivity.
So you don't download the block chain, share the public keys with the server and ask the server for incoming payments and to relay outgoing payments?