Does an iOS app have the ability to set iOS Safari cookies? My specific interest is in the context of the Facebook for iOS app, but it can be asked of an iOS app really.

Given all the recent changes to Facebook and the way that Facebook cookies are not cleared when you log out of Facebook I've become keenly interested in knowing how my access patterns to Facebook can result in tracking cookies sticking to me.

What I'd like to know is: if I use an iOS application, like the Facebook for iOS application, can I end up with session cookies set in iOS Safari that relate to Facebook? Or are all login cookies related to Facebook completely contained to just the Facebook application?
The iOS security sandbox prevents App store apps from writing to the Safari app's data directories, including wherever Safari writes cookies.