A gun listed on a Form 4 is the standard transferable gun. If your state allows you to have an MG, one that's on a Form 4 is it. No dealer licensing is necessary to own it. If you have a Curio and Relics license, the gun can be transferred to you from Virginia to your state without going through a dealer, which saves you the $200 transfer fee (seller to dealer: one fee, dealer to buyer: another fee), and leaves you with only one fee (seller to buyer).
Can't say it wasn't done, but I haven't seen a 34 that was full auto only. A lot of long time owners have had their guns before books and information were readily available, and they only know what someone told them long ago. As we all know, some people will gladly tell you more than they know.
Regarding the questions about the receiver, send the seller an email, but don't be surprised if he really doesn't know what he's talking about.