But the video evidence would not be admissible in court!

It would be admissible in court if a lawyer was given it and took on the case. But what lawyer with balls big enough to fit in the court room would sit in front of the judge and explain the case.

Oh they were, you just ignored the third option. The 17 intelligence agencies (today, as DHS did not exist back then) have a rocky relationship ever since Watergate. Rewind the circumstance mentally, that they have surveilled American citizens, highly illegal before the Patriot Act, and even under said act, a supposedly trustworthy and secret FISA court judge gives the approval to spy domestically on an American citizen.

Ergo, he recorded his boss's wrongdoing with the plan, that in the ideal case he can get his hands on the recording, and has to answer before a military tribunal, he can blackmail higher ups into getting him out of the mess, since Reynolds had bosses too. That's why he stalled with the FBI to avoid charges of criminal conspiracy, and to pin all blame on Reynolds. His actions are actually in line with that of North in the Iran-Contra hearings, deny any involvement publicly. In real life, many of the people handling sensitive data don't retire, they get retired, so it was a spur of the moment life insurance policy.

I live in the Gordius Apartment Complex, my interior designer was M.C. Escher.

Except that the FBI guys clearly thought he was not being smart for stalling while Reynolds was dead. So I'm not sure if that's what's being implied.

They gave each other alibis as to what they did in the truck (and overall, being the only survivors) and with Brill gone, they did not have to admit to anything beyond what authorities can prove. If a federal law enforcement employee gets charged, they're represented by a government lawyer, so the character's motivation might have been this: even though the FBI seized the evidence, defendants and their lawyers have the right to access it, and he (or both of them) made the Xanatos Gambit, that their lawyers will know, for who they actually work for, and press the top brass into giving them immunity by painting the picture, that Reynolds had hijacked a routine training, and the black ops guys worked for Reynolds, not the NSA.

The tactic would have worked, since federal law enforcement agencies don't like external probing, and would stonewall the other agency. Just remember, when the ATF was forced to reveal just what went wrong in Fast and Furious, and they submitted a 900-page document, that was mostly redacted, and that was post-9/11 and to the Congress. The truth is, that the CIA and the NSA has a condescending relationship toward the FBI, and it comes as no surprise, that they aren't keen to share any intel with the Counterintelligence or the Counter-terrorism unit of the FBI despite the Patriot Act practically forcing them to. They view the FBI since Watergate as cops view internal affairs.

In context the FBI guys have thought he wasn't smart for stonewalling, but that's just forgetting how 18 minutes are missing from the Watergate tapes (by "accident) or how North claimed to not recall anything. They aren't sorry for doing it, they're sorry for being caught, and FISA has established a wall they seemed unnecessary to work efficiently. The problem is, that RICO still managed to get the right guys without the need to spy on every Italian Americans, and they don't accept this, because they're not detectives, and so they fail to make to the right connections. Reynolds claimed to not being interested in who does coke or cheat on their wives, but the character of Black is actually the closest to outed NSA agents who rather listened to private internet porn (or played World of Warcraft) rather, than actually follow up on suspected or verified terrorists.

I live in the Gordius Apartment Complex, my interior designer was M.C. Escher.

I don't think it really matters what happened or happens in real life. Jack Black and the other tech guys were presented as rather silly and his behavior during the interrogation together with the reaction of the FBI guys only seemed to confirm that. He may have started recording because he was panicking, but I don't think he had this whole preconceived plan to take down his bosses.

Within the universe, the relationship between government agencies have closely resembled actual life.

I get momentarily panic, but their actions in the interrogation room was calculated, they banked on the NSA covering their own hide, and save them in the process.

I live in the Gordius Apartment Complex, my interior designer was M.C. Escher.

I'm afraid I have to disagree with you. Like I said, the tech guys specifically are portrayed as rather foolish and I don't really see anything in that interrogation scene that suggests otherwise. Their behavior doesn't seem calculated to me. I don't think the FBI guys would've mocked them like they did if that's what the movie was implying.