Before I even go any deeper, I want to say that I am also of the stance that the OP should just find a way to get it initialed, whether that's stopping by, or whether it's having them mail/fax him a copy and he just sends it back.
That said, as an example from the ATF FAQ
"Q: Who must comply with the requirements of the Brady law?
Federally licensed firearms importers, manufacturers, and dealers must comply with the Brady law prior to the transfer of any firearm to a non-licensed individual.
[18 U.S.C. 922(t), 27 CFR 478.102 ]"
Basically, the law is a limitation of the gun dealer...not the gun purchaser (State laws notwithstanding). The FFL is responsible for ensuring that the form is filled out correctly, and is required by law to ensure that all transfers from them are done as required by statute...
That's why there's a 'gun-show loophole' because it's a law on DEALERS of firearms, not purchasers. A purchaser of a firearm has no requirements to fill out paperwork to buy a gun, but a gun dealer has a requirement to have paperwork filled out (in this case a federal form) to SELL the gun. As long as the purchaser doesn't LIE on the form (Which is something that applies to any federal form, not just a 4473) he should be perfectly fine.
Of course, the gun shop, and the clerk themselves COULD get in trouble for failing to abide by the law of having a fully and correctly filled out 4473 that doesn't indicate the buyer is prohibited from owning guns, and yet still transferring a firearm.
That's been my understanding of the code anyways, and if anyone that disagrees can find a part of the code that contradicts me, I'd love to know.
Once again though, that all said? Just go and initial the form, or find a way to get them an initialed copy if it's a long drive, no reason to mess around with the shop over a silly mistake.