Of course, this being the future, everything we see could also be an artist's impression of what happened, a trivial little visual simulation for the benefit of the court. But we don't really have to go that route.
All the events are seen from the Klingon POV, basically: the boarding at the eye level of the boarding party, the explosion from the outside. The data would probably be of Klingon origin, then, found in the databanks of the BoP.
The BoP survived the incident and was in the hands of Kirk. The briefing on Genesis, now updated with narration by Kirk himself, is also something Kirk would be in possession of. So the issue of interest is how all this material went from Kirk to the courtroom. Might have been Kirk sent it, to defend his case in absentia. Might have been the Klingons then requested its use; might be they intercepted what Kirk sent and used it without asking anybody pretty please.
Timo Saloniemi