Your question applies to both real amps, or modellers...the 'source' of the tone is irrelevent.
Are WE, as guitar players dialing/creating our own sound???.
YES, and NO...to a certain degree.
It doesn't matter, if one is using a Marshall, Soldano, Peavy, or a Line 6 XTPRO....our own signature comes from the fingers, and way in which we play...For example, I could duplicate Dave Gilmour's rig to the tee, but I'd never sound exactly like him, no matter what...and HE wouldn't sound like me, using my setup either...
Music and tone, comes from one's psychological bent...no two people can have the exact same psyche.....
I also think, that for the most part, subconsciously, we do tend to emulate tones/sounds that we have heard (and like a lot) in the past from others....so, we often use that 'mental recall' as a starting base, and then 'tweak' from there...
Modellers, are simply used as a 'convenient' tool, in order to obtain a variety of different amp sims/tones at an affordable price.....they don't offer one any more opportunity to create unique sounds, than any other real amp would...
Every musician is 'unique'....so technically...YES, we are dialing in our own sounds......but, of course, that sound (no matter the gear used) has many influences....
So, to summarize, I would say YES & NO!
KEV