You are absolutely incorrect.
Show me the law that says only citizens can own NFA items - there is no special regulation in the gun control act of 1934 which specifies permanent residents or citizens. If you can buy a regular 4473 FFL item (any serialized firearm post-1968) and silencers are legal in your state, a permanent resident can buy a silencer, most typically on an eForm4 from a local dealer.
Similarly, a permanent resident can buy an NFA item, short barrel rifle (SBR, sub 16" barrel, rifled barrel, serialized firearm) on an eform4 from their local dealer, as long as the category of SBR is legal in their state of residence. A permanent resident in a state with few or no firearm restrictions such as Idaho could buy an AR-15 or AK/AKM semiauto action based based SBR. If the permanent resident is in a state with restrictive new assault weapon laws, such as WA, they could still buy an SBR, but it has to meet the other requirements of their state of not being a state-prohibited assault weapon (such as a 10 inch barreled bolt action chambered in 8.6 blackout, as bolt and lever actions are exempted from the recent WA state assault weapons ban)
That same theoretical permanent resident can even own what's casually called a double stamp item, two NFA items attached together, such as putting a silencer on an SBR, if they have enough money to buy both, pay the $400 total in NFA item tax stamps, and pay their local FFL SOT dealer for the transfer. Exactly the same financial cost to them as for a US citizen.
If you buy it online, it will go on an eform3 shipped from the originating vendor/manufacturer/dealer to the inventory and books of your local FFL SOT, and then an eform4 to you.
https://www.atf.gov/firearms/docs/undefined/atf-national-fir...
https://www.atf.gov/firearms/docs/form/form-4-application-ta...
You can see the "paper" version of the ATF form 4 there.
An alien admitted to the united states under a nonimmigrant class visa generally may not purchase firearms (except under certain exemptions) or NFA items. A permanent resident is an immigrant class status.
Quoting the ATF form 4:
Alien Admitted to the United States Under a Nonimmigrant Visa. An
alien admitted to the United States under a nonimmigrant visa includes,
among others, persons visiting the United States temporarily for
business or pleasure, persons studying in the United States who maintain
a residence abroad, and certain temporary foreign workers. These aliens
must answer “yes” to question 16.d.1 and provide the additional
documentation required under question 16.d.2. Permanent resident aliens
and aliens legally admitted to the United States pursuant either the Visa
Waiver Program or to regulations otherwise exempting them from visa
requirements may answer “no” to this question and are not required to
submit the additional documentation under 16.d.2. An alien admitted to the
United States under a nonimmigrant visa is not prohibited from purchasing,
receiving, or possessing a firearm if the alien: (1) is in possession of a
hunting license or permit lawfully issued by the Federal Government,
a State, or local government, or an Indian tribe federally recognized by the
Bureau of Indian Affairs, which is valid and unexpired; (2) was
admitted to the United States for lawful hunting or sporting purposes; (3)
is an official representative of a foreign government who is accredited to
the United States Government or the Government’s mission to an
international organization having its headquarters in the United States; (4)
is an official representative of a foreign government who is enroute to or from
another country to which that alien is accredited; (5) is an official of a foreign
government or a distinguished foreign visitor who has been so designated by the
Department of State; (6) is a foreign law enforcement officer of a friendly foreign
government entering the United States on official law enforcement business; (7)
has received a waiver from the prohibition from the Attorney General of the
United States.
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You will note that the 4473 and the form 4 has a section for citizenship. Theoretically, a Canadian with permanent resident status typically provides their citizenship and alien number as part of the application.
See also, questions 35 through 38 on the FFL application form, which asks if you're an alien admitted to the united states under a nonimmigrant class visa. The FFL application form does not require you to be a US citizen. It does not allow for nonimmigrant class visa holders to be an FFL. Again, a PR is an immigrant class person.
https://www.atf.gov/firearms/apply-license
https://www.atf.gov/file/61506/download
Further reference: https://www.atf.gov/firearms/federal-firearms-licensee-quick...