I don't think Nameless is going to try to betray them going forward. At least not for the time being. My guess is that the in-game Nameless betrayed them because his impression of them was that they were trying to lord their power over other people, because in-game Cyril basically hired them to basically harrass somebody, which is basically his berserk button due to his own past. Of course he's still going to fleece them for all he can get, but then he'll turn around and sell them out because he doesn't like them.
But in this case, the message Cyril has sent Nameless is that the family acknowledges that the guild and the folk living in the slums exist, and that they don't look down on them in the slightest (which is probably why he was careful to specify that the money was not to buy slaves, but to pay their parents' debt). That's a very different first impression to make.