Here's my credible link (I presume that a link to the ATF documentation on Federal Firearms Licensing is credible enough for you?):
http://www.atf.gov/publications/download/p/atf-p-5300-15.pdf
Check page 3:
Background Checks
You must conduct a National Instant Criminal Background Check System (NICS) check or appropriate State background check for each and every sale or other transfer of a firearm to a non-licensee. The NICS or State background check ensures that any person who purchases a firearm from you may lawfully possess firearms. A NICS or State background check MUST be conducted before:
* The sale or trade of a firearm;
* The return of a consigned firearm;
* The redemption of a pawned firearm;
* The loan or rental of a firearm for use off of your licensed premises; or
* Any other non-exempt transfer of a firearm.
Failure to conduct a background check has a significant impact on public safety. You could be fined, have your license suspended or revoked, or be prosecuted.
So yes, background checks ARE being run at gun shows. Granted, there are still private transactions going on, but they are definitely in the minority.
You should try checking out a gun show sometime. You might well find it enlightening.

What is the point of rules that are not enforced?