Now, time for a question. if you are Platinum, does EF ALWAYS show you all the C inventory available to you? And if you are EXP, does the EXP desk fairly consistently have enhanced inventory over what EF says?
EF has no way of knowing your elite status since you can't enter it in the query probably because the GDSs and AA have no way of dealing with it even if it saw it, so what you see is the inventory for the masses.
My experience as an EXP has been that it is rare that C, or any other upgrade/award inventory, opens up when requested beyond what EF shows. But YMMV depending on route/date/time, when the request is made relative to departure and of course whether or not the RM gods are in a good mood or not.