Well, in the examples here neither the payer nor the payee has a lightning channel. For instance, Fedi to Ark via Lightning. In this case who is actually "settling" on LN? Maybe the fedimint and the the swap provider?

As far as the mint user and the ark user, their trust models haven't changed no matter what is the state of the lightning channel that was used to link them.

So the mint has an open channel with someone and boltz has a channel with someone else (or maybe even they have a channel with each other). They are responsible for managing that channel just like any other lightning channel.

The people who want settlement have the same level of settlement (or trust) as they had when they started, and which, presumably they accept.