Are you talking about when he filled out the 4473? I don’t think that counts as “being compelled… to be a witness against himself.”
Exactly. The stated purpose of the form: "will be used to determine whether you are prohibited by federal or state law from receiving a firearm."
That's not confessing to a crime. It's giving the FFL and FBI information to be used in making that determination. Generally, answering "Yes" to any question/s except for
21.a. "Are you the actual transferee/buyer" will likely get your purchase request denied.
To cite another example, if you make $50,000 through some unlawful enterprise or activities, like gambling in Hawaii or selling drugs, you must still report that income when you file your income tax returns. Filing a false return is a felony. What you did to obtain that income may only be a misdemeanor. However, the IRS is not going to initiate an investigation into your illegal activities based solely on the information on your return.
Having said that, if law enforcement is investigating you, they may obtain your returns, which may be used as evidence of your unlawful activities. But, that just means the agency already had evidence you were breaking the law -- hence the investigation.
There's a legal reason government forms are required to inform you of the purposes, uses and consequences of not providing the information requested. They aren't allowed to use the information you provide for any other purpose, including filing charges for acts you included on the form.
It boils down to one thing:
answering truthfully that you use drugs is stupid. If you already know in advance you will be denied by answering "Yes", why are you even submitting the form?
Lying on the form by saying "No" might get you that gun, but you just committed a felony.
I also understand that making any false oral or written statement, or exhibiting any
false or misrepresented identification with respect to this transaction, is a crime
punishable as a felony under Federal law, and may also violate State and/or local law.