Tyres do play a big part - on a long track with many corners like the Ring.
My first 3 Ring weekends with the CSL were running on PS2s - and i was up to an ok enough pace by then circa 8:40 average BTG during TF sessions.
I tried Cups for the first time on my 4th visit and immediately i dropped 20 seconds on a lap. Ok, i also had APs fitted by this stage but i do not feel that the brakes contributed much in the way of reducing the laptime, just that the brakes did not judder or overheat anymore!
Slowly been 'nibbling' away at BTG times since then...