The technical issue, as far as I can see, is simply that Keynote itself (and not iOS in general) does not support the standard Bluetooth "Human Interface Device Profile". This is a standard that defines basic keyboard and mouse input for Bluetooth, and is what devices like keyboards use. It is also the profile that some third parties use for alternate devices, mapping things like cursor controls and mouse clicks to other bits of hardware, like a handheld clicker.
Instead of supporting this common standard for Keynote remote control, Apple seems to have intentionally chosen to create its own solution, one that only works with iPhones. I say "intentionally", because the HID profile already works on iOS in general (which is why, for example, any third party Bluetooth keyboard works), and it would seemingly entail effort on Apple's part to prevent it from working in this case.
(This is also why I am dubious of Ginny's claims -- as far as I know, Apple has not released/licensed its proprietary Keynote remote method to anyone else, and no standard Bluetooth profile works.)
So in short, Apple could fix this situation with almost no effort, by allowing Keynote for iOS to be controlled by the standard HID Bluetooth profile, just like it is on OS X. Support for this profile already exists in iOS, so it would only be a matter of letting Keynote "listen" for such devices when in presentation mode. If Apple did this, a huge array of third party Bluetooth clickers and controllers would be available to presenters. Until it does so, we're stuck with only the iPhone.