I wouldn't be upset. I'm another one of those people that drags my ropes all over the place. She was assertive with the horse in the beginning because the horse is clearly not the most sensitive to people pushing towards it. Its the kind of thing that you can use "gentle" steady pressure all the time and have the horse lay into it because you want to be nice, or let it be known what you are doing and in a matter of time, that horse won't need any pressure at all. Its funny, everyone loves those horses that respond like your shadow, never running into you or dragging too far behind, but no one ever likes the little things to get them there. The trainer was taking her place as a leader. When a horse doesn't get out of the way respectfully when the leader is asking them to move, they don't gently push, they bite. Just because the horse was quiet doesn't mean that it was attentive to the situation, it was getting reminded.
As far as the rope goes..... seriously? You can call me a sloppy trainer if you like, it won't hurt my feelings whatsoever. If my horse manages to hurt itself out of something as simple as a rope laying on the ground, I haven't done my job in training that horse. Yes, it is safer when training to have a long rope, especially when desensitizing. If that horse were to lose it for a minute, you have to get it as far away from you as possible for your own safety. If that horse isn't the lightest to pressure, which the horse in the video wasn't, you need a heavier lead. If you have that big heavy lead bunched up in your hand (even if its not wrapped around), unless you are a bear of a person there would be too much bulk in your hand to have a good grip if the horse were to bolt.
To the OP, you are the one that sees the horse, if the horse is making progress, then do what works. I've had plenty of people bring horses to me where traditional methods had failed. They question what I do at first because it doesn't follow what they've always been taught. It doesn't take long to remind them that obviously, what they had been taught wasn't working, so it was time to try something different. I'm not saying that the horse in the video is a difficult horse, what I'm trying to get to is that you need to listen to your horse, not a bunch of people who have never interacted with it on the internet. That horse is in a good frame of mind. She is communicating and trusting that trainer, She is learning to be aware of her surroundings, and obviously that horse is far less concerned about that rope on the ground than all of the people here. Horses don't follow peoples rules, they follow leaders.