Personally I think the watermarking on this video is a little obsessive, but my opinion doesn't matter. I'm asking a hypothetical question, what I think or what the news channels actually ends up doing isn't important.
If they actually had removed it (for whatever reason, justified or not), would that be legal?
I think so. If I remember correctly I saw this footage on another site yesterday without watermarks. I think it was taken by one of the human rights workers and then was used by several news agencies who put their won watermarks on it.
If they actually had removed it (for whatever reason, justified or not), would that be legal?