On the TV, the "expert" cops they interviewed are back to saying that it was a B&T and that "It is such a rare pistol that only a few gun stores in the country sell them."
I mean, they're expensive, but even my LGS has them, though they mostly carry the PDW types. I suppose sales are small enough that the ATF could trace it, depending of course on the state where the shooter lived. If they wanted to find out if someone bought one at my LGS, if the buyer had a CCW, they never got a NICS check, and the ATF would have to physically go to the store and pull all the paper 4473s (because my LGS thankfully refuses to use electronic 4473s) and hand sort them one by one.
EDIT: Disregard the background check comment. I'm only on coffee #1 and forgot the tax stamp. Which, if the shooter had an IQ above 50 and wanted to avoid being traced, would lead us back to what Dogmush posted.
Military Arms Channel:
https://youtu.be/ul-l0jEgkwA