Not buying it Dan. Every racetrack I have been to and every race I watch on TV, the track gets faster once some tire rubber gets laid down. Thus everyone wants to qualify last.
I think any loss in time is either a function of the track changing with cones moving or being put back where they belong for timed runs or the heat of the day reducing HP, not grip. Tires are happy well into the 200 degree range which is never achieved at an AX, but is probably exceeded in a QDE which would result in loss of grip, but only because the tires are being overdriven and overheated. Slow down and cool the tires and the grip would be back.
So those are my caffeinated hypothesis.