Yeah, a person - bodyguard or not - is restricted by the laws of the land. However, just pushing your way through a crowd is not assault, or half the Christmas shoppers would be arrested. Similarly, standing in the way and blocking you from proceeding is not assault. If the guard’s behaviour on private property is not appropriate then the owner can ask the person to leave - like the restaurant owner will take the paparrazzi’s side over a patron’s…
I assume too, grabbing someone’s camera by the lens when it’s pointed at you is not assault, unless they then hit you with it. They would have to grab your person. If them grabbing your camera makes you get into a dispute with them which distracts you from approaching the subject - bonus.
Blocking your way on a public beach or other public property may be “creating a disturbance”, but then the question is, what happens next? If you try to go around them, do they grab or punch you, or simply keep moving side to side to stop you going throughy? If you then deliberately try to push past, using arms, that would likely be assault - by you.
I suspect the good bodyguard is well trained in tactics and the law. A frustrated, slow-thinking fan (or political protester) is unlikely to be cool and use logic - so the trick is to eascalate it calmly until the other person makes the first inappropriate move. Having another bodyguard who will swear to that probably helps.
I suppose if you wanted to test the theory, you would find a public place, assemble a group of 10 or 20 friends who did not mind being beaten up and a couple of camera operators standing inconspicuously in the distance. Spread out about 4 feet apart, and slowly try to walk past the bodyguard. See if he loses his cool. See if 2 or 3 bodyguards try to take out the ringleader. See if you can find 10 people crazy enough to try this who won’t lose their cool either, won’t hit back no matter what happens.
Of course, he could always pull his gun and say he was being threatened by a mob…
But - even if you have video proof - if the DA (not influenced by rich people and ex cops, of course) decides that ust challenging the guy and his boss was sufficent provocation to justify a small amount of force, then who’s going to prosecute? Ditto for suing - can you afford as many lawyers as the other guy?
Might makes right; or the golden rule - “he who has the gold, rules”.