Is his finger on or off the trigger? Seriously, I can't tell. And in this instance anyway, it is probably perfectly OK for the finger to be inside the guard...the gun is obviously pointed downrange, and the instructor is likely checking his hand position, and in order to check certain things like how much finger you're using, you kinda gotta show 'em, right?
The camera? We do live-fire exercises all the time with a remote camera downrange.
Now, that said:
"EARL, YOU DEAF SON OF A ****, I SAID 'PUT THE DANGED GUN DOWN!'"
Mike