The defense did not want the information from the State, because the State did not have it. They wanted the information from (IIRC) the FBI, which owns the database.
Yes, to get this information the DT would need to get a subpoena from HHJP and then file it with the court in the proper jurisdiction. I see what you meant by litigation now--if there is an objection, that would be litigated in the other court.
The prosecution is not hiding this evidence. The prosecution does not have it. Neither does the defense. I'm not sure what you mean by rights of audience, but the SA would have no greater ability to obtain those documents than the defense, because the FBI is claiming intellectual property rights and refusing to release them.
I said early on that if I were the SA I would have done the out-of-state subpoena myself and obtained that database (if possible) to avoid any appellate issues due to the DT's incompetence in not obtaining it. But it certainly was not the SA's job to do this.