H. A very interesting case. What is you take?
I'll introduce another angle, does a business parent have a non-disputable right over a subsidiary regarding an operational matter? Probably yes.

The parent company must comply if appeal is dismissed, it must order the subsidiary, but the subsidiary operates under another jurisdiction which can forbid carrying out the order.

There are web sites giving advice on setting up email accounts with non-US companies who have no US based servers. Ironic that people may be setting up email accounts that may be subject to, for example, Russian law.
There is always Switzerland.