I think you'll need to cite chapter and verse, my friend. JC Devine is offering a variety of Thompson submachine guns for auction, and has this note on their page:
CLASS III / NFA WEAPONS: In all transactions, all NFA rules and regulations will apply. Class III firearms may be purchased by private individuals in many, but not all states.
California is one state that prohibits possession of machine guns by non-LEOs. New Hampshire does not. You pay the $200 transfer tax, and get a federal background check, and then you can take delivery if your state allows it.
Obviously, the prices went to the heavens. And it means that no NEW full-autos will be sold. That, regrettably, includes the XM-8.
And if the weapon was manufactured and on the civilian market prior to May of 1986. (someone correct me if I'm wrong, but I'm thinking that milsurp MG's not already on or intended for the open market at that date cannot be sold into civilian use regardless of date of manufacture. I can't afford one at todays prices anyway.)
No full autos manufactured after passage, existing guns can be still be transferred to citizens, with Uncle Sugars permission of course and with payment of the transfer tax.
The chapter and verse is pretty short US Code Title 18 section 922 (o)
(1)
Except as provided in paragraph (2), it shall be unlawful for any person to transfer or possess a machinegun.
(2)
This subsection does not apply with respect to -
(A)
a transfer to or by, or possession by or under the authority of, the United States or any department or agency thereof or a State, or a department, agency, or political subdivision thereof; or
(B)
any lawful transfer or lawful possession of a machinegun that was lawfully possessed before the date this subsection takes effect.
The law took effect May 19, 1986. Now while it would seem any gun transferred via the Tax Stamp process would be "under the authority of the United States", but that is not what the author of those line intended when he inserted them at the last minute (almost literally) into the bill that became the law, and that is also not how the BATFE and the courts are interpreting them.