There is no human right to not have it discovered a person purchased a firearm that was later used in the commission of a crime.

In the same sense that there is no human right to not have it discovered that a car that ran someone over is registered to a particular person, or that a plane that crashes into a neighborhood was scheduled to fly under a particular flight-plan and be operated by a particular pilot.

In general, society (American society included) assigns additional responsibilities of care and auditing to ownership and operation of machines and equipment with a high probability of causing the death of a third party if they are mis-used.

If you are implying that people have a right to privacy, sure; except American law makes far more important and sensitive information a matter of public record. Things like home and car ownership are entirely public as it is. While you could argue that this shouldn't be public, there's still valid reasons for those things to be tracked in a central database. Likewise, I can think of valid reasons for why the government would need to know who owns a particular gun.

If you are implying that a lack of a functioning Form 4473 index protects the right to bear arms... I'm not sure I agree with that. If the federal government really got a bug up it's butt about banning private firearm ownership, they wouldn't need a Form 4473 index. They would just need to ban the manufacture and import of new firearms and/or ammunition, and let the now-grandfathered old weapons trickle out of the market - no need for a gun grab.

This is how they banned fully-automatic weapons, after all. You can technically still buy them, but the cost of a grandfathered automatic weapon is so astronomical that you would never dream of actually firing it.