Have you tried modifying the appvar from xLIBC on-calc? Try with two different appvars that contains the same data, one created directly on-calc and one created on the PC (or sent from the calc to PC then back to the calc)
This seems pretty odd because I never heard of read-only apps before, unless it's a CSE-specific thing or a bug? Someone who got more knowledge on TI-84+CE appvars might have to investigate.
By the way, the HP Prime has a type of variables (not local nor global, but rather program/app-specific) that cannot be edited by anything else than the program it was created with.