I see both sides to this:
One one hand, if he is showering at an edge of a parking lot, with only a few gallons of water, that is one thing.
However, I am concerned about one point, which related to the tragedy of the commons: What would happen if everyone did this? No, it isn't expressly forbidden, but shouldn't this be done in a park or at least off the road, rather than in an urban area where the gray water may result in lawsuits against WM, calls to the city/state/Feds about biological contamination, and may other things... especially areas where RV-ers are disliked already and the local populace is looking for reasons to ban overnighting in their area.
Common sense comes into play. Just because it isn't expressly forbidden to do an action, doesn't mean it should be done. Peeing on the back of a WM building isn't forbidden, but people just don't do that.
The gray water thing may not be much, but it can be enough impetus to get politicians involved. To boot, the Youtuber in question has a very popular channel, so it is assured that the local city council and other politicos where that WM is have seen this. This does not bode well.