Contracts only bind the people who are party to them, so they couldn't go after the publisher on the same grounds. And there is a lot of case law around suing publishers so they probably know they would lose a lawsuit on other grounds (and maybe get an anti-slap ruling against them which could cost a lot of money).

One thing I don't understand though is I thought arbitration could only award monetary relief? I didn't realize that they could issue injunctions like this which I thought constituted an equitable remedy.