Because the issue is with the 4473. Also, it does not matter if the form was filled out or not, as shown with the recent case, but if the form was not filled out, it could be more of a problem.
The FFL was told that the firearm was for the husband, then suddenly the wife has it a short time later. It is one thing to not say that it is a gift, but another to say that it is not a gift, then suddenly a different person has it.
Regardless of whether there is a conviction, it can be looked into.
Filling out the forms does not negate issues with the 4473. Yes, if it were a gift, then it would be ok. No form filled out which also indicate a problem. She brought in the firearm, which is documented.
Yep. In some cases the BATF does not seem to care about straw purchases, in others they do.
It would be nearly impossible without self-incrimination to prove the gun was bought as a straw purchase. The husband does not have to tell the FFL it is a gift at the time of purchase.
Regardless of whether there is a conviction, it can be looked into.
The only way I can think of is if DOJ pulled all his purchase records and saw a pattern of him gifting guns to his wife. Still, that would not make sense because if he filled out the spousal transfer form all laws are still covered. If he did not fill out the forms for other guns then it is back to the couple being able to keep silent and there would be no proof any un-documented transfers took place.
I've seen ATF come around and ask about potential straw purchases. I know of one couple where the wife paid for and filled out every 4473 for guns and NFA items while the husband played with the guns. ATF thought they were doing straw purchases do to the volume of guns they were buying based on NICS checks. ATF looked up every single transfer in several A&D books and then went over to their house to find the guns. Every single gun was in the house.

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