Yes, the video is clearly fake.
Why? Because the left took a legitimate video and edited it to make it LOOK like a bad green screen attempt then push it right out in front of us knowing some on the right would scream about another fake video while posting it everywhere.
Anyone who thinks this is a video that was legitimately put out by the news media is very very short sighted, you are playing right into their hands. They will use this as another example of how the right only see conspiracies.
The clever double-reverse fake theory makes a lot of sense. Or is it a triple reverse fake with a half twist?
Actually, what you posit makes the most sense. It might just be a working level stiff who thought “Watch this...I will toss in some obvious fakery for them to catch and we will have a great time watching them get into a lather over it.”