Going off to disguise my motives in the characters, I realize that Basil wants to talk to them because as Tam's fellow students, they are in a unique position to endanger him. On the other hand, he doesn't want to flag that. (I'm not sure that he even knows that Susan has recognized Tam and told his story before the other students met him.) So what is his excuse gong to be? For that matter, how is he going to persuade Vera to let him do it? He could tell her the truth, but that would not necessarily mean that she would accept it.
Not to mention that I'm thinking a man with a gun in his hand -- and stymied at what, exactly, in this story constitutes a man with a gun in his hand.