Why not?
I'm not sure by what you mean "at least for a shift." The counter-charge tactic and the shift tactic are two completely different things.
Just to make sure we're on the same page, here's what he's talking about:
There are two monsters: monster M and player P.
P readies an action to charge monster M when monster M moves.
No, we were not talking about that.
We were talking about
P readies an action to shift (or move) away when monster M moves next to him. Monster M charges (instead of move and attack).
The advantage of P's ready action is that if M were doing a normal move and attack, M is now 10 feet away and cannot attack, even with a charge (charge requires 10 feet).
AAs contention is that since M still has move left over as part of his charge, he can continue to move as part of his charge. My contention is that just like normal move when a foe finishes his movement next to a PC and is now about to attack, his move action is over, his standard action is about to start, and the PC's ready action shifts the PC away.