Not only did 5 small monkeys in a trench coat make this ludicrous statement, but the ESA doubled down and embarrassed themselves and Microsoft in the process later on with a written statement that sounds even dumber, and even more like a threat towards anybody running private servers than anything else.
In a statement to PC Gamer, the ESA wrote that, so far as it's concerned, "Private servers infringe on the intellectual property (IP) rights of game publishers. Publishers reserve the right to exercise their rights against them."