He has the game in his library, so all your responses is just assumptions.
And even if he had pirated the game before, he shouldn't be banned from online when he actually do purchase the game.
The same can be said if a thief stole a product. If he got busted, he would still be able to buy the product again at a later date and get the full enjoyment out of it.
OP, are you sure you haven't joined a ranked match in your first game and left?
If you leave ranked matches you get a temporary ban (15 min)
Probably not the case, just making sure