and what gives you the impression they can't contain channelers?


Rand was protected by the ancient agreement, and the doorway he went through has no payment requirement. The Snakes answer questions and sniff the questioners. The End. From what we've been shown the Snakes can't harm anyone who goes through their doorway because they can't break the agreement. They shied away from the fire. I don't see that as good evidence that they are powerless against channelers. It just means they hate fire. Maybe their form of shielding requires that they capture the person the way Moiraine was, and they weren't allowed to do that. The Foxes can harm people because people have to bargain for their gifts.

We've seen no channelers go through the Fox doorway except Moiraine and Lanfear. After they made their bargains, and there was no way to leave, the Foxes were allowed to do whatever they wanted that was within their powers. There's no evidence to show they can't contain a channeler once the ancient agreement is null, and plenty to show the opposite (because that's exactly what they did).


Furthermore, what would Moiraine have done if she could channel against them? If she'd killed them all she would have gotten lost and died of starvation.