Yes, and that’s normal. Let’s say you’re in court for murder. If you argue “I was elsewhere fighting my old enemy Foo”, Foo may not want to confirm that, but a court can still force him to make a statement in court. It isn’t different between companies.
Also, technically, it’s the court that subpoenas, and not “to back up your claims” but to get a good enough view of a case.
They will allow questions, insofar they give more insight to the case and aren’t too damaging to those being subpoenad.
“court rules may permit lawyers to issue subpoenas themselves in their capacity as officers of the court. Typically subpoenas are issued "in blank" and it is the responsibility of the lawyer representing the plaintiff or defendant on whose behalf the testimony is to be given to serve the subpoena on the witness”
So, yes, it seems Apple’s lawyers, acting in their capacity as officers of the court, can directly issue subpoenas. They’re not acting as Apple’s lawyers when they do, however (in theory. Feel free to think whatever you think about the ‘in practice’ part)
