Right, and as with amps in general, a tone that's created using a guitar with Humbuckers, for example, will sound as it was originally intended when using a guitar with Humbuckers. Is that specific to the profiling process? No, though it's a factor to consider in the reproduction of a particular snapshot of an amp as it was originally intended to sound.
I agree, but your statement was still wrong:
> There's also the issue of the guitar and type of pickups used to create each one of those profiles.
The pickups are NOT used to create the profile - meaning they do not have an influence on the profile - which is what you want. Different pickups will sound differently using the same profile.