If iOS's filesystem is case-sensitive then why can't I save a.pages and A.pages? When I try to save document in Pages.app on iOS with the same name but a different case I get: 

"a" is already taken. Please choose a different name.


I would expect that this would work if iOS is case-sensitive.
HFS+ is not case-sensitive.  It is, however, case-preserving.

Your problem is not a problem, it is working as designed.