I never said parallel was safer, it's just that trying to achieve that right off the bat can screw beginners up IF they don't have the flexibility to so. I think we agree on this point.
What I'm referring to in the video is the level of control in the descent, the video of yourself was much better. Sorry I'm not going to buy that the stronger you get the faster you're going to drop into the hole. I'm going to estimate that the guy in the first video can probably perform a perfect 600-700lb back squat, he just wanted to see how much weight he could actually move. And yes he bounced his hams off of his calves and his belly off of his thighs just like bouncing on the bench press to achieve that, but that's what you do in olympic lifts to catch cleans so it transfers anyways.
Here's me squatting 405, this is about the fastest I think a person should descend into the hole especially on a max attempt irregardless of ROM.
Ideally it would be even more controlled than that. You can see in both of our videos there's atleast some control in the descent and there's no bouncing, and that's what beginners should be trying to do.