You're right, in most cases they do know exactly what they did and are just lying.  But sometimes mistakes do get made and people are wrongfully banned.  That's not the norm, but it does happen.

This is why I suggested including in the ban PM one example of the plagiarism offense, which would obviate their need to start threads like this and having members dig up an example for them.  That wouldn't stop the pleas-for-mercy threads, but it sure would help reduce ones like OP started here. 

It just wastes people's time having to prove to the plagiarist what they already know to be true, and then after an example is shown, inevitably the next thing they do is try to make excuses or beg for a second chance.  You'll see.  If OP returns to this thread, that's exactly what he's going to do.