Nope, the "custodial" is between the same person's two nodes. This is not a custodial wallet in no part.

Both legs of the channel are owned by the bridge operator, who is one person.

So the payments goes through like in a bridge and it's completely trustless.

Alice->Charlie's Liquid node-[hosted channel]->Charlie's Bitcoin node->Bob

No one has to trust anyone in this case. For Charlie, he receives L-BTC on liquid side and sends BTC on Bitcoin side and charges a fee for the service. It is atomic. That's all.