Fargosgirl explained what happened accurately, imo. If one watches attentively, one can see that Linda didn't lose her temper, or get emotional about the horse being frightened, bargey, etc., a good example being when she stood stock still & lowered her head & bodily energy, mirroring the horse when the horse came down off the adrenaline, shown by his standing still & lowering his head.
Also, this was a demonstration for Level 1, gunsels/newbies who are only learning to stay safe & keep the horse safe. For Level 1/kindergarten, it was an adequate demo, since a horse ignoring humans as possibilities of being its leader, thus not respecting their bubble, & right-brainedly trying to leave & find a horse alpha was kept safely with the handler (Linda, who had to take over for owner). One eye only compounded the danger, of course.
The horse could've been handled with more finesse, more inner potency from any number of developed horsemen (Pat could've calmed him down w/ more finesse), but no Level 1 student can be expected to emulate those higher levels, so as a Level 1 demo, it's fine, except for the fact that once they put the horse safely out at end of rope to stand in his "box", Linda failed to instruct as to how to then get him from the box to point B. Eventually, one has got to move one's horse. ;)