They did. Cullen would probably fare better than Leliana considering the Templar thing.
That's what I'm thinking as well. I think I heard Alexius say something like, "Where are your assassin's now!?!" during the battle (unless that was Dorian, but I don't think so. I'll have to go back and listen some more.) So I don't think we'd be sending whichever advisor in there alone in this case.
So maybe, if you send Leliana, she takes a few assassin's with her, but they get caught and killed, and she is subsequently tortured. If you send Josephine, maybe she brings a few other diplomats with her to broker an agreement? (Although I don't think that would end well... or maybe she's not an option in this case? Could be possible). And if you send Cullen, then he goes in with his forces (templars? warriors? a mix of both?), and he ends up being the best choice in this situation. Or maybe he also gets captured and tortured. Who knows?