OK now THAT is complete bullshit.
Even in the most-used chokehold of all time--you guys have seen it in the UFC endlessly--no, only ONE arm is across the neck. It is the one applying pressure as your choking arm hand resides in the crook of your elbow as you squeeze.
In a guillotine choke--probably the other most-used--only arm is actually making contact with the neck.
That guy is a bozo.