Generally, the video is true. But I have some exceptions.
This is worse on a front wheel drive then a rwd. The weight of the car, end to end, makes a difference.
They made the statement the driver can feel the slippage on the front, and not the rear. A good driver and feel the rear slip.
The video with both cars on the track at the same time is a bit deceptive. The front car did not correct steering and held steady state. The rear car WAS steady state, the changed. Watch closely, the driver tweaked the steering, throwing the rear out and causing the problem.
Some maintain the front must have steering protection. Some say that the front tires will kick up debris that could damage a worn rear tire that would have survived with a new tire.
What about stopping? New on the front will be better. What about accelleration traction? FWD or RWD.
Generally speaking, they are correct, but sometimes it is not the case. Try stopping on a curve with any car with the better ones on the rear. Severe disapointment will follow.
I also am suprised to note that they do not recommend replacing tires in sets if the safety is that drastic. It is always better to rotate the tires and then replace 4 at the same time.
Does this imply that tires 1/2 worn are always unsafe, if all 4 are worn? Of course not, but the implication is there.
What about cars that are heavier on the rear? That will change things quite a bit.
Just some things to think about. Again, they are basicly correct, but there are some glaring variations to consider.