The thing is, while there were only roughly 7,000 FG42's produced, there were only ~240,000 FJ to ever serve in WW2. Given that the guns didn't start getting into the units until 1943, that means that there was one FG42 to every 34 FJ. But given that plenty of the original FJ were gone by 1943, and that plenty more were supply/pak/other non-infantry jobs, one FG42 per squad would be a realistic figure. That also means that they could have centered them into Sturmtruppen, or spread them around like an extra BAR-kinda thing.
Basically, sure it was a rare gun overall, but since it was only issued to the FJ, and the FJ were only ever a small number of active troops, it was still about as common as the BAR or Bren was for Allied infantry.