If you fly around the world at 35,000' (or 6nms altitude), how much further do you travel than doing so on the surface? On the back of a virtual fag packet, difference in circumference is 2xPie (R1-R2), ie 2 x Pie x 6=38 miles. In terms of circumference of 25,000 miles, about 0.15% difference.
I've not heard of 'True Ground Speed'. Did he confuse it with 'True Airspeed'?