When reference letters are requested, does this say anything about the chances of getting an interview?
An assumption to my answer: That a school is exercising the (imo correct) decision to only ask for references from a limited part of the pool to save everyone time.

It says something but not very much.

I've been on several committees where letters are only requested from a limited subset of candidates, but that subset is fairly broad. It's not necessarily just the short-list, because letters factor heavily on who makes the short list.

Mainly, it says you have a chance, instead of no chance, but no more than that.