Except...that's exactly what happened. As shown, most of the CIA's "breakthroughs" were bullshit, either lies from the detainee to make it stop or lies from the CIA to cover their ass. The FBI got good intel and didn't lie about shit.
You think a guy who knows if he admits to his child porn collection he's spending the next few decades in a solitary cell to save his literal butt doesn't have huge incentives to not confess? The guy who's facing the death penalty? Dude, I put people away for DECADES and they confess. You know why attorneys say don't talk to the police? It's because we are trained to get the truth by convincing you it makes sense to tell it. Torture is training to get someone to talk.
Terrorists are not super humans or sub-humans. They are not immune to psychological techniques. They are, for the most part, extremely sheltered people unfamiliar with life outside of the one thing they have been taught. Once captured, they are nothing but ignorant men who are WAY out of their comfort zone, in a completely alien environment, often poorly educated, disoriented, alone and vulnerable. Interview rooms are bare because you have nothing to think about while you wait for your interviewer except your own actions that led you to be there. It's a RELIEF when another human enters the room, even if he should be your enemy. You want to be his friend. Treating them like a monster reinforces your alienness, it gives them something to hate you for, it confirms their prejudices. No one gets confessions that way, that's TV bullshit. You get confessions from empathy (usually feigned), from offering socially acceptable ways to confess, from painting silence or denial as worse than admitting the truth, etc.
Detectives know this, or at least the good ones do. POWs will attest to it as well. Its way harder to lie to a 'friend' than it is a guy who's an asshole. Its even harder if you can find a common enemy. I've had people say "I know you're doing good cop/bad cop"....and it still works. It's not because people are stupid, its because humans are wired a certain way, and you can take advantage of that if you know how.