The problem seems to be that Rod's reasoning in the linked pdf file is not consistent.
In one case he allows for the reduction in IAS with altitude but in the other he doesn't. From his own reasoning, both TASs increase but by less than the reduction of IAS due to altitude, so in fact both IASs reduce.
Using his own example, he says Vx at SL is 69KTAS (which is also 69 KIAS). He says Vx at 10k is 75KTAS which (using his 'math') would be 62 KIAS.
So both IASs reduce with altitude, but Vy decreases at a faster rate until it meets Vx.