I've re-read Tom's post and you're correct - He's asking if he should remove the paper BEFORE he wraps. (It sounds like he's wrapping anyways but wants to know if he should leave the paper on.)
Simply put, I'm saying that he can leave the paper on if 1) the mfgr. will warrant the siding with his 'stated layers' underneath the siding, and 2) if so, and the paper is still in good condition, leave it up and go ahead and wrap. Unless I'm being misled, house wrap is an air filtration barrier. When installed properly, air+moisture is allowed to 'escape' from the house but it's prevented from entering the house. With 1) and 2) being Yes, in this example, one isn't changing the 'operation' of the house by adding the wrap. Moisture shouldn't get trapped with the wrap. And with vinyl siding, inside air+moisture should be able to 'breathe out' a whole lot better than with the 'old masonite' siding. So with all things being given a 'green light', he should be fine to leave the tar paper up and wrap the house. As I previously wrote, I can't see the condition of the paper so I have to leave that to Tom. If it's in good condition and warrantable with the siding mfgr. leave it. There shouldn't be a 'double vapor barrier' here because, as I see it, he's had a 'double vapor barrier' all along.
You're right - To remove the paper is NOT a hugh issue. And you're right, he can just do it. BUT, does he HAVE to do it, IMO, no. I understand your point about interior vapor barrier and the exterior one (the paper) but, again, it's been there all along. If there's going to be any rot, I think he'd see it, or at worst, 'find' it when he goes to nail up the new siding (or wrap the house.) Yes, IF he's going to leave on the paper, he might want to do a little more inspecting BEFORE he gets going. (I'm not sure but I think I said that in my 2nd follow-up ...)
If we're disagreeing, that's OK w/me. If we're agreeing, that's ok w/me too. I just can't say more w/o actually making a visit to the house to see if what he wants to do, or not wants to do, is 'OK' w/me.