Do you seriously not see where they say you were using unauthorized hacks/scripts/exploits? It's literally right there in the first response you got.
After some investigation,** I can see there were hacks/scripts/exploits used on this account and we had to take action.** The account was benefiting from these things, and given the information we have, I can't remove the ban on the account. This action is only taken when we find things that give a competitive edge over others.
And yes, using unauthorized 3rd party programs can get your account permanently banned.
The following are examples of behavior that warrant disciplinary measures:
......
ix. Using any unauthorized third party programs, including mods, hacks, cheats, scripts, bots, trainers and automation programs that interact with the Software in any way, for any purpose, including any unauthorized third party programs that intercept, emulate, or redirect any communication between the Software and Riot Games and any unauthorized third party programs that collect information about the Game by reading areas of memory used by the Software to store information;
Straight from the Terms of Use, Section 5 titled CODE OF CONDUCT.
There is nothing wrong going on with Riot's player behavior team. You asked for why you were banned and they answered it for you. You continue to ask for why and they simply say that they have already told you, which is true.