This is as TL;DR as I can make it while still being convincing. There are multiple reasons to my knowledge why the hornet uses tires at the size it does. To keep things simple, the larger rear tire will increase the size of the contact patch and long story short you will have more grip. You are correct, a smaller tire handles better and makes the bike require less lean to hold the same line, BUT a heavier bike with more power simply cannot get away with this. On a smaller tire, you will have:
Cold shearing, where the cold rubber literally gets ripped off the tire due to so much force going into such a small contact patch.
Tire overheating, both localized and overall, due to the small contact patch being instantly overheated and the smaller tire overall not having the surface area to dissipate the heat.
Suspension - As you may not know, tires make up a huge component of the suspension, and to keep it short, putting a small tire on a big heavy bike compromises that. You would need more pressure to make up for the smaller tire, which further exaggerates the contact patch issue.
Overall wear - not much to say here, you have less tire running a higher temp. it's obviously going to wear out faster.
Now to be honest, do I think you'll crash if you put on a 160? No. Maybe if you were really pushing it on a track balls to the wall you'd start to see why a wider tire is necessary. If you wanna try a 160, i'd say go for it.
Disclaimer: I am not a tire expert, I'm just sharing my OPINIONS
And to explain that video, that bike is specifically designed to turn left, and those guys on sportbikes are probably sandbagging because it's an event to show off the left turning bike =(