[Tom Servo]

The whole intent of "actual purchaser" is to make sure the person filling out the form is keeping the gun.

Nope. This is from the 4473 itself:

For purposes of this form, you are the actual transferee/buyer if you are purchasing the firearm for yourself or otherwise acquiring the firearm for yourself (e.g., redeeming the firearm from pawn/retrieving it from consignment, firearm raffle winner). You are also the actual transferee/buyer if you are legitimately purchasing the firearm as a gift for a third party.

ACTUAL TRANSFEREE/BUYER EXAMPLES: Mr. Smith asks Mr. Jones to purchase a firearm for Mr. Smith. Mr. Smith gives Mr. Jones the money for the firearm. Mr. Jones is NOT THE ACTUAL TRANSFEREE/BUYER of the firearm and must answer “NO” to question 11.a. The licensee may not transfer the firearm to Mr. Jones. However, if Mr. Brown goes to buy a firearm with his own money to give to Mr. Black as a present, Mr. Brown is the actual transferee/buyer of the firearm and should answer “YES” to question 11.a. However, you may not transfer a firearm to any person you know or have reasonable cause to believe is prohibited under 18 U.S.C. § 922(g), (n), or (x)

Right or wrong, who is paying for the gun is the issue.

I'd let the FFL decide if this was okay with him. Given the fact that the only part of the "purchase" that is legally important is the transfer, I can't see the problem.

It's not going to be OK with the FFL, and he would be right to refuse the transfer.