Agree, they may have been able to narrow it down to a Sig, but not a specific model. I just have difficulty visualizing how they would be looking for a specific model of Sig, additionally if true that may have helped the investigation very early on.
Purely hypothetical on my end, but maybe they knew it was a Sig by the marking on the unspent round, and when they came across RA's name they could have checked ATF records and found he'd purchased one in 2001. Then they may have simply asked him if he still had it.
JMO