If you are talking about False Bans, I can't really speak on that matter as I have no knowledge of it.... it definitely happens though.

Yes there have been a few false bans (10 that I know of) but a lot more are people kicking off and hoping Bungie will let them back in or playing innocent in the hope Bungie thinks that "yep they made a mistake they did not know about". Too many times when pushed for info or even when looking into their game history the truth comes out. "I did not know cheat engine was active" "I did not know that this program did that as well because I use it for something else" "It was not me playing" "I was hacked" "I did nothing".... and what about the 7 Trials wins with no opponents. Ohh look same players in different matches time and again and look at those win/loss against them. If they think it is a false ban that is why there is a appeal form.

That's a good point, I'm pretty sure they run with the notion that all bans are permanent so why is there even an appeals section.....

Bungie manually investigates every case but admit mistakes are made. They are just being fair to players giving them a second investigation to see if something was not picked up in the first. Ps. Who told you the bans are permanent a banned player can play again after a set amount of time....... 500 years.