Theoretically, a disqualified person (felon, etc.) can "purchase" a weapon (that is, acquire the equitable title). He just can't take possession of the weapon. The determination of disqualification is done at the level of the transferring FFL.
The FFL could, again theoretically, hold it for him until the disqualification was removed (by pardon and records expungement, for example).
In general, the gun laws are focused on "possession" and not on "ownership." This is especially important regarding NFA items. Dealers become bailees for extended periods of time, awaiting bureaucratic approval of the transfer. During that long delay, the purchaser is the equitable owner. The dealer doesn't have the right to sell (or use) the item out from under him.
Not everywhere.
From gun hating California:
CA PC 29800 (a) (1) Any person who has been convicted of a felony under the laws of the United States, the State of California, or any other state, government, or country, or of an offense enumerated in subdivision (a), (b), or (d) of Section 23515, or who is addicted to the use of any narcotic drug, and who owns, purchases, receives, or has in possession or under custody or control any firearm is guilty of a felony.
To gun friendly Idaho:
CHAPTER 33
FIREARMS, EXPLOSIVES AND OTHER DEADLY WEAPONS
18-3316. UNLAWFUL POSSESSION OF A FIREARM. (1) A person who previously has been convicted of a felony who purchases, owns, possesses, or has under his custody or control any firearm shall be guilty of a felony and shall be imprisoned in the state prison for a period of time not to exceed five (5) years and by a fine not to exceed five thousand dollars ($5,000).
With 50 State, multiple local jurisdictions AND Federal laws governing firearms, never assume a law here applies to a transaction there, nor that a Federal law isn’t more lenient than a local one. Unlike the kid in the OP’s post who didn’t do his research, always consult the most recent laws where you live to be sure you stay out of the pokey.
Stay safe.