By default, iOS keyboards cannot interact with other parts of the app/their container app, and cannot send information over the network. [1][2][3]
If you do enable full access, then yep, anything is fair game. But that's a tradeoff users can make.
[1] - https://twitter.com/SwiftKey/status/514540356918972416
[2] - http://swiftkey.com/en/blog/swiftkey-require-full-access/
[3] - https://developer.apple.com/library/ios/documentation/Genera...