A tyre isn't a simple, rigid 2d shape. When it's under load, the tyre distorts and sidewalks bow out. The distance between the wheel axle and the road reduces, which reduces the effective radius of the wheel.I'm happy to hold my hands up if wrong, if an inner tube is totally flat then the volume is very small, however we aren't measuring area, we are measuring the rolling radius. You could get small variation where a point on the tyre perimeter is dragging behind the corresponding point on the rim, but this woud be cancelled out if the tyre is only exposed to force in one direction.
The effect is more significant if the tyre is under inflated. At its extreme, a completely underinflated tyre will flop about at the edges while you drive on the rims - a very small wheel with rubbish grip.
Ironically, the best explanation I've seen for this is on a 4x4 site
www.4x4Tirereview.com/airdown.html
Shame on you Linf!
Mickle still did speeding though.