Surely what most pilots mean by "groundspeed" is the distance over the ground (i.e. the Earth's surface) covered in unit time. Therefore, the fact that you may be at altitude and cover a longer distance by virtue of your distance from the centre of the Earth is irrelevant. Otherwise your groundspeed becomes a function of altitude.
If you want to be pedantic with the physics, nobody seems to have mentioned Einstein's relativistic effects of both General and Special Relativity.
The general relativistic effect will mean that because gravity is slightly less up there the aircraft clock will run faster than it would do on the ground, and this is countered by the special relativistic effect of high speed motion which means that the faster you go, the more time slows down.
It is quite possible with modern atomic clocks to demonstrate these effects in aircraft.
So every time you go flying, so long as you don't fly too fast, you are actually aging slower than you would do on the ground.
Yes, the clock will run faster but at an altitude of ONLY 30,000 ft the effect would be so minute that only an atomic clock would be able to recognize it... a very accurate atomic clock at that!
Altitude plays a big role and I'd say the biggest in factors with regard to groundspeed. If you're on the earth and are travelling at 100mph, your groundspeed is 100mph. Simple as that! If you're travelling at a higher altitude, since the earth is round, as you travel you will cover less distance over the ground than you will in your flight path through the air. Then you could go into how the earth is actually slightly stretched at the equator because of it's spin and all that ridiculous stuff. Seeing the earth from space or the moon confirms that the earth is a pretty damn good sphere and the stretching effect is soo minute! Taking anything more into account than the altitude of the aircraft for groundspeed is just a waste of time and is not really relavant. I drew a little diagram posted earlier in this thread illustrating the effect of altitude.