Have you explained why you want the gun checked out?
If you do so, the buyer may be more amenable to meeting you half way for a check to be made. If not, you can ask why. If he still refuses to justify his stance, you can go with either "he has something to hide" or "this sale is obviously not that important to him"
By that stage, you can decide for yourself if the gun in question is worth the punt.
As for the guy, well, innocent until proven guilty. Morally speaking, only you can decide if you are comfortable with the present situation.
Sounds a bit like extortion to me, trying to extract a lower price.
Extortion is a bit strong. Negotiate is the word I would choose.
If there was an aspect of a purchase that meant I could loose all the money I'd paid, I would certainly try to mitigate.
Rather than extortion, the OP is perhaps being willing to give another person he knows nothing about, the benefit of the doubt, despite failing to get assurances that this purchase is sound....
If very few people actually bother with firearms police checks police, then that might be why many firearm thefts go unresolved and unpunished...