The question Which is correct? do they? or don't they? or have they or haven't they? was summarily closed for reasons that aren't clear to me.
Personally, I don't think it's necessarily obvious that the "polarity" of an assertion is "reversed" by adverbial elements such as hardly, rarely, seldom, and to my mind that's what the question is effectively asking about.
It's true the question as presented could also be seen as asking whether the tag question after They hardly have X should be have they? or do they? But there are no comments asking the OP to clarify whether that might have been his main concern (vanishingly unlikely, imho), so I doubt that was a relevant factor in the closevotes.
I think the question should be reopened. (Well - having answered it myself, I would, wouldn't I? :) But if there aren't another 4 users who agree with me, perhaps someone could at least present a convincing argument as to why it was simply dismissed as "Proofreading" or "Lacking in detail". At time of writing this request, I'm baffled by the closevoters rationale[s].