There's almost never incontrovertible proof in a criminal trial. Even if the suspect is on camera confessing. The sheer number of people who confessed to crimes and were then found innocent through DNA evidence is perturbing.
The primary responsibility of a defense attorney isn't what a guilty defendant wants (to get off the charges), but it is to ensure that their client receives an absolutely fair trial with all the fairly-obtained evidence fairly presented.
Having watched a few FBI interrogations and other true crime related videos there certainly are such proofs.
I have a few of these come to mind, like the dude who killed his ex, took the house surveillance cameras down after the facts but didn't know they were backed up on servers, he was caught with the cameras in his truck shortly after. Most of these publicly known cases have a ridiculously long trail of proofs actually
I'm not saying mistakes don't happen, they obviously do, but in many cases it's extremely easy to prove if someone's guilty or not.
> Even if the suspect is on camera confessing.
That's not enough in most countries