I think both parties have been leaning a bit on Judge Lester's Order on State's Motion for Protective Order which has been reaffirmed by Judge Nelson which allows redacted discovery of undisclosed witnesses' identifying information. For instance, since the beat-down video O'Mara alleges would presumably contain identifying images of prospective witnesses, I assume it would be redacted under that order though I suppose someone could ask the court for a transcript of the video.
Very good point, and I should have stated the details as I understand them, so as to not cause confusion here. What is available in the courthouse is papers filed in the courthouse. Discovery details are not filed in the courthouse, except what may appear as exhibits actually attached to courthouse filings.
State's evidence is subject to state sunshine law - but I don't believe defense evidence falls under the same umbrella.
So, assuming the video is on the phone, it is discovery, and it is originally in the state's hands. You can't get it at the courthouse because the court doesn't have a copy of it, and there is no duty to give a copy to the court. Anybody can demand turnover from the state, but past press efforts at this were stonewalled by Corey with bogus legal arguments. I know this due to having been in direct communication with a member of the press at the time, and reviewing and commenting / criticizing / suggesting counterarguments to the state's stonewall.
On top of that, I absolutely agree with your observation that the state will also lean on Lester's order. Anybody (other than the defense) who wants to get a copy of that video from the state will have to litigate to get it, and that's not cheap.