Well, if that is his sole reason then I think he is overlooking several things.
First, does he ever or has he ever purchased a firearm from a dealer? If so then the GOV already has more information than a GFL application will give. (Other than the SSN that is not required for NICS, the GFL application is kept at the local probate court instead of a national database, and it simply allows a person to carry a handgun so there is no record of a person actually owning a firearm)
Second, as former military the GOV already has his fingerprints and other identifying information in their records.
Third, using a credit card or those shopper discount cards will reveal more to the GOV than the GFL will. The GFL only shows up to the authorities during the fingerprint check, after that the application is kept at the probate court (flow of info stops). With the current level of data mining where it is, the GOV knows far more about those people that use credit cards than they would a GFL holder.
Fourth, the GFL allows you to carry anywhere in the car. Frankly the only thing worse than the GFL restrictions are the ones if you do not have a GFL.. (keep it in the console, glove box, similar compartment or in plain view) Plain view means absolutely nothing can cover up any part of the gun.
If this guy refuses to obtain a GFL because he believes the US gov't has no business regulating the possession of firearms by private citizens (which he's absolutely right), I'd bet he obtained his firearm(s) through inheritance, gifts, or private sales. I'm sure he would never want to fill out that lovely little yellow form (or is it white now?) that "registers" a firearm in his name with the gov't for the next 20 years.
I've chatted with these types on-line. They are the ultimate fighters for the U.S. Constitution. They act in ways that are consistent with their beliefs, even if it means they could be arrested. I respect their convictions and only wish I had the cajones to follow in their footsteps. But instead, like most folks, I have my GFL and follow the law, even when the law infringes upon my constitutional rights.
"I am free, no matter what rules surround me. If I find them tolerable, I tolerate them; if I find them too obnoxious, I break them. I am free because I know that I alone am morally responsible for everything I do." - Robert A. Heinlein