What I'm wondering is if this means that banned users are still using the forum with new accounts because that seems to be the only way they can receive this message and request to have their old account unbanned.
There are/were sufficient cases where the banned users either bump their appeals, send us PMs from time to time, talk off-forum to other members about their forum account, etc. There are several legit ways banned users could find out about this thread. However, I suggest people circumventing their ban through another account to try and come clean about everything.
This change gives people who committed plagiarism and got a permanent ban, a third chance, not a second chance.
Not really. That would imply being pardoned and repeating the offense. The possibility of appealing a ban from the "good for the forum as a whole" perspective did indeed already exist - IIRC signature bans were added in support of this back then.
This thread acknowledges the possibility of an appeal and also provides a more clear guideline, all wrapped in a Holiday spirit fashion.