It's been more than 10 years since I saw this, so I may remember something incorrectly, but I'm not talking about cutting fingers. That wasn't the ultimate torture scene, or if it was, it was the warm-up. I can send you a DM of what I mean if you like.Back to Man of Fire, do note that Denzel shows no pleasure in his acts (though he's slightly mocking his very evil victims) , he's not sadistic, he just wants to find and save the kidnapped girl, at any cost to the bad guys. All the more as she was his responsibility, his watch, and also, somehow, his only and last friend.
I find it interesting that you seem to argue moral justification because Denzel's character took no pleasure in the torture and that he was trying to save a girl. That's just the kind of false dichotomy that allows the poisonous Hollyweird brain worm into your mind.
I believe torture is always wrong because if you don't limit what you're willing to do, you'll eventually become as evil as your enemy.