The ASP has to bridge the transaction, but it’s little different than what an LSP does. If your LSP doesn’t want to fulfill your payment, all you can do is close your channel. They are required in your oath either way.
Ark transactions can be channels in the same way and can be paid with the same dynamic of having to go through the ASP, but still acting as a normal Lightning payment.
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The bridge is trusted.
Users of the same Ark can pay each other similarly to Lightning, but to get into the Ark in the first place (either via Lightning or yet another Ark that has to use Lightning) the ASP is the spender on the inbound swap and can collude with itself.
A chain payment to the Ark may be trustless if you can afford it, but again that's pointless as you can just open a channel, which is why they have to scam and call it Lightning for poors.