This article's correct. Most guns used in crime are indeed sourced by criminals through already illegal means. The majority via straw sales, which background checks, however expanded, cannot effect as the straw buyer can pass the check, or transfers from people (often illegally) possessing them already aware of the transferee's prohibited status. Since in both cases the suppliers are already willing to break transfer laws, it's inane to think they'd do any expanded checks. Particularly since such checks are absolutely unenforceable in practice, as there is no way to discover, much less prove in court, that a transfer occurred absent a confession (which still creates a "they said/they said" situation), unless it is witnessed and probably recorded by law enforcement in the act.

The only possible group any expanded background check might impact is the theoretical case of a legal possessor unknowingly selling to a prohibited person, but there's no evidence that is a significant source.