Wouldn't it be a self-incriminating testimony, though?
No. But if either side had a concern about self-incrimination of some frivolous 'wrongful termination' action down the pipeline, Depp would just execute a document waiving his supposed rights to sue Disney for any testimony that they would give as well as executing a stipulation of confidentiality that whatever testimony given can not be used in any other Court proceeding. It is pretty common place in civil lawsuits where the testifying party is "professionally paranoid" that their testimony might incriminate themselves or their company in some future proceeding.
Also in a civil suit, testifying witnesses cannot plead the fifth unless the testimony would expose them to criminal prosecution, and there would be no criminal liability against Disney if they testified that they had chosen not to work with Depp because of the OP-ED. Pleading the fifth is baseless if it is for the purpose of protecting one's self from civil liability.
But even civilly, Depp would not have any valid basis for recompense against the studios should the allegations turn out to have been false. That tab gets picked up by the defamer. Studios can openly refuse to work with (and/or stop working with) actors/actresses based solely on believing in allegations of misconduct/abuse. Studios have done it before right in the open even where the actor denied the allegations and the evidence presented as more circumstantial in nature.
That said, if it was a concern or disney execs were just, well, "professionally paranoid", Depp's lawyer would get that waiver of rights document signed and a stipulation of confidentiality in place because ultimately that is testimony Depp's lawyers want to elicit and that would be it. Disney would not be able to resist subpoena. Even though Disney has a "sovereign status," they are still subject to subpoena.
On the flipside, the grounds for a wrongful termination action against Disney is so baseless that Depp's lawyers would not be willing to sacrifice/greatly weaken their more substantive defamation claim against Heard to maintain the possibility of a half-baked wrongful termination claim against Disney. In a multi-million dollar lawsuit Disney would not be left out from the witness list unless they did not have favorable testimony to give.
Heard's lawyers, in fact, have already sent a subpoena to Disney for records, including "all documents concerning any decision to cast or not cast Mr. Depp in any future Pirates of the Carribean films":
Whatever documents Heard's lawyers obtained through that subpoena would have also been turned over to Depp's lawyers as well...so Depp's lawyers probably decided not to call anybody from Disney in to testify because the documents contained information which is highly unfavorable to their defamation claim, and now they're just trying to wing it with Depp's star power and second-hand speculation through coterie of friends and workers .
