Personally I think the demotion to mod was the correct thing to do, its not as if he lost his rank completely, he can still staff, its just he can no longer use admin commands, which were the commands he abused.

Why would they allow him to carry on using certain powers he abused? if anything now he is mod again he can gain trust and work his way back up to admin.

And lets not forget he did abuse once, but twice using 2 different commands, he then also lied and tried to carry on the lie by forging proof, granted he did then tell the truth after but it shows he was willing to carry on the lie.

Overall with the things he did i believe demoting him to mod was the correct thing to do, it means he doesnt have access to the commands he once abused and that being mod, he can regain trust from the staff team to apply in the future