I can guarantee that is not true. I have direct personal experience with several cases where the offender was investigated for, arrested for, and successfully prosecuted for violating 18USC922(g)(1), and there was never any consideration given to whether or not there was a violation of state law. In fact I've worked in states where there was no prohibition on the possession of ammunition by a felon under state law, and offenders were arrested/prosecuted under 18USC922(g)(1) for possessing ammunition, but not a firearm.I've never heard of a single case where someone was arrested just for being in violation of the fed PP statute; that statute is always invoked as an add-on after a person violates some state law.
It is foolish/reckless to suggest that someone would not be arrested/prosecuted for violating 18USC922(g)(1) unless they were also violating state law, as that is simply not true.