AFAIK in many states there isn't a paper trail for secondhand guns in many cases and if they were bought before a certain year (60s?) there often is no registration as such. I think it has to have been bought from a shop recently to have one but of course there are different laws in different states to some extent and they aren't big on anyone having records they will show to the government full stop.
I guess they're scared of it being a slippery slope so to speak and ending up like here where you have to apply for you license stating which calibre weapon you intend to own, its use and show you have somewhere suitable to fire it.