Well, as you said, the police gathers evidence after arresting the person. The rules as for this network say that whoever says "I hack" even as a joke, is guilty. No further investigation, no disputes, no removal from the record, no chance to become a moderator, and further bans are prolonged, just because of a sense of humor that the staff dislikes. Certain people even end up getting permanently banned for a cheap little joke. I am 99,9% sure that if the staff was to take a look at the players who "admitted to hacking", they would find that a great, great majority of the people were just joking.
Why cannot staff treat "i haz mlg hax mannnnn" the same way as they treat TS pokes about hackers? Follow and look at the damn person before heading straight onto the ban panel. It really is worth it, considering you will be keeping more legitimate players, and only end up throwing out the actual cheaters. I'm just gonna say this: If people keep getting banned for "admitting to hacks" in the process of hacker elimination, all that will happen is that a large group of legitimate players will disappear at the same time.
Let's assume 1/3 "admitters" actually do hack, even though I believe the number is way lower (this could actually be a good idea to research). When 3 people are banned for admitting to hacks, 2 of them will be legitimate players. In the long run, you could be looking at a removal of 1000 hackers, and 2000 legitimate players. What you have done is to make the hacker:legit ratio go in the favor of hackers, as there will be less of them removed. If you want an effective way to not have a hacker in every single game, I suggest not removing the innocent players who at least create a certain balance to the servers.
I used to be a mod back in the day myself, and obviously had to follow the guidance given by Sr. Staff, which lead to me banning tons of people that I knew were only playing jokes, trying to make other people laugh. I knew a lot of people used this system to get people they disliked banned. All they had to do was to ask them "DO YOU HACK!?!?!?", and they would answer "ya d00d i haz tha faze mlg noscope hax client". A screenshot of that, and BOOM, he is out. At last, the fact that I no longer wanted to be a party pooper, ended up being one of the reasons affecting my decision to resign.