I guess there is a certain comfort level in seeing a CHP when selling a long gun. I believe the requirements are to try to ascertain that the buyer is not disqualified from owning a long gun; i.e., not insane, not a felon, maybe something else I can't remember. If you have a CHP, or a PPP, and you show it to me I believe I can rely on that to have met the requirements. If you don't, I will probably still sell you a long gun if you tell me you are not disqualified from owning one.
If a buyer has a CHP, why would they not show it, as an act of good faith? No recording, no bill of sale, just here it is and it's not expired. (Hell, if it's expired I'd still sell a long gun because you passed a background check recently. Unless of course you were babbling insanely or telling me you needed a gun quick to off your wife's lover(s).)
Edit note: I take bait easily.