A lot of wrestling technique is whatever you want to call it. What you call a bow and arrow, I've heard referred to as a Gable Turk. When I hear bow and arrow, I think head in the ribs attempting to lock up an inside cradle(poor technique IMO). What I saw in the video was simply poor technique. He had about 3 things going on top and not doing any of them well. I saw no resemblance of a cross face cradle other than the fact that he did have a cross face. If anything, maybe attempting some sort of butcher?(or whatever you want to call it). When he reached back for the toe, it did nothing to improve his chances of turning his opponent other than inflicting pain.
When it comes to back and/or head injuries, the trainer is always going to error on the side of caution. They don't want to get sued and they aren't doctors. Unfortunate way to win or lose.