couldn't a group of artists have found that very old ivory and carved the figures much, much later?

I can't envision any way that carbon dating could disprove that proposition. If I understand how carbon dating works (and I don't), it only tells you when the thing you are dating (must be organic) died, because that's when it stops producing that form of carbon. I'll try to look into the intricacies of dating man-made artifacts more this week.

(And no off-color puns about "dating man-made artifacts", please -- my wife is not a cyborg, as far as I know)