Unfortunately it is a common occurrence for fakers to use ASNs and names included in Ebay groupings. I see fakers purchase groupings off of ebay, and then magically a capture paper and pistol appears with the grouping.
The biggest red flag to me is that I have never seen a legitimate papered bringback MG on that form. The standardized form you show references circular 155. Circular 155 was issued on May 28th 1945 and specifically prohibits machine guns from being brought back due to obvious concerns. I have seen papered MGs from this time frame, but they were all special forms and were all brought back by officers. I would not expect a tech sargent to be able to bring something back like that. Of course, a lot of stuff was snuck home in duffle bags.
Below is a direct quote from the circular.
b. The following items are prohibited by
3.b (3) in circular 155
• (3) Firearms of the automatic type (or
component types) such as machine guns,
submachineguns, or any type of gun which
a number of shots or bullets may be
discharged with one continuous pull of the
trigger.
The entire circular is well worth the read because it talks about a lot of interesting things, like the trafficking of war trophies being illegal.