First of all this has nothing to do with iOS/Android. This is an app trying to access a web service. Apple needs to provide oath or similar for accessing their iCloud services.
>> And also, for installing $0 apps you don't need any credit card details at all. Even the buttons are different "Install" v/s "Buy".
This is untrue. I couldn't download any free apps until I had setup a merchant account with credit card.
I know it's not. I was just hinting the plus sides of a competitive product, something the new users should know, and something Apple should learn from. It's less about the app, and more about what the app is allowed to do, yet.
>> This is untrue.
No, it's not. You mean Google asked you to setup a "Merchant" account for being a "customer" of $0 apps? ... Think again. :)