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I suspect the actual issue is that the publisher is not a party to whatever contract there exists between the author and Meta.

Unfortunately for free speech, it is no longer the case (if it ever was) that publishers have strong financial resources compared to an increasing number of those who want to hide things.

You don't need an expensive lawyer to point out that the publisher is not covered by the arbitration agreement, a cheap one will do.

The bullying is not possible because the argument made is weaker, bullying is possible because the argument is made by a party with fewer resources.

Bingo. Authors are easier to bully into submission.

They are defending the author in this case though. Im sure they bully authors plenty too, but I'm pretty sure they keep some around for allegations of libel and other complications where they have the authors back.