When Slughorn tells us about the Black brothers [...] I rather got the feeling that he was speaking in terms of Slytherin the House, not in terms of his club.

Oh, that's right! He was talking about Slytherin (at least, I think he was). I was talking about joining the Slug Club, which now that you've reminded me, was open to Sirius no matter which house he was in. I wonder if Slughorn did recruit him then... you know, since he couldn't have him in his house, he could at least have him in his club? Too bad we don't really get any indication one way or the other.