Or they brought back the ball, edited and copied it to other balls or even a different artifact, and sent the numerous copies out.
Or maybe the ball CAN transmit video, but requires a mage to transmit it post recording, and is not something a soldier can do.
Or maybe the ball can do anything whatsoever, which makes the author an utter idiot.
Like you, I can imagine a hundred different ways it could all play out. Stomping out one of them is always a better move than doing nothing, even if the results end up being the same (because you can't predict everything). That's called risk mitigation.
There is evidence it works like a video camera, because they clearly recorded the "kidnapping" from the ball the soldier was holding, and we've seen the King watch a fight that happened in the past from a ball just like it. At the very least, that means the ball can record and playback video. Why the heck would you have 2 balls that look the same, and one just records, and the other just displays? Sure maybe they had such a dumb magical artifact, but it is more reasonable to assume it's one device that does both.
The orb may or may not have been in the ship fight (somewhere hidden from view, for example), but that doesn't matter. It was there in the assassination and throne scenes. That's solid and direct (vs circumstantial) evidence.
As for whether it can transmit video, there is no solid evidence, only conjecture on your part. We don't even have an accurate grasp of time lapses in this show, so using those as "proof" doesn't hold water. For example, in your "summoned to the castle" scenario, what if news traveled by messenger or some other magical means, and the orb physically traveled with a soldier at around the same pace as Naofumi did (he would have left later because he got summoned after the King heard the about what happened) and arrived at the same time or a bit earlier than him? That would also explain why the King was watching the video while Naofumi was there (because he just got it).
Does this matter? Not really, because it's all conjecture. Compare that to the very highly probable chances (as I explained above) that the orb can record and display video, and it's clear which one is more likely to be true.
[Note: I only say "very highly probable" (vs factual) because anything is possible. However, saying otherwise ("those are 2 different orbs with different functions!") is like claiming you are innocent in a court by saying your long lost identical twin did it.]