That video does not show any problem, where is the headshake?
They are trying to prove that the bike is not susceptible to kick back and tank slappers but they don't seem to understand where the kick back comes from

Please advise why the steering induced wobble has nothing to do with road induced wobbles?
I'll try and not make this too technical.

Please ask if you lose me.
Let's work with a mechanical model:
Your bikes steering physically works like a pendulum: It tends to center itself. It will swing until it's slowed down by friction and centered again if you disturb it.
In the video they disturb the steering by an input from the handlebars. Then they leave the system alone and it does what it is designed to do: The steering geometry and damping of the tire calm down the movement quickly. Every bike will do that, not just a BMW.
Rider / handlebar induced oscillations are rather harmless because your arms have a rather high damping rate and they aren't very elastic. The steering needs a continuous input like turbulent air flow from a leading car or truck or your fluttering jacket to keep a wobble going and simple things like loosening your death grip on the bars, shifting your weight or tapping off or accelerating will quickly cure the wobble.
In our model your arms resemble a very stiff shock absorber. The one end attaches to the pendulum (the steering), you push or pull on the other end.
Pushing / pulling will deflect the pendulum. The high damping and stiffness of your arms in death grip will slow the pendulum down considerably. The steering will take more time to return to the stable & straight position, the bike will start to change its course (like you pulling on the bars to initiate a turn). If you pull on your bars periodically and alternatingly your bike will weave from side to side.
Now we look at the steering and your tire:
Here the situation is completely different. The tire is rather flexible and pretty much likes to behave like a rather soft spring. (Ever seen some high speed footage of a tire going over a bump?) Internal damping is something a tire ideally should have in oodles but you have to build it in using intricate combinations of rubber with layers of fabric and belting made of Kevlar or steel. Too much internal damping and you have a rather uncomfortable fork lift wheel
You hit a couple of potholes - off centre:
Imagine you push and pull the end of a soft spring attached to your pendulum (you grab the tire by its contact patch and twist it against the steering):
Depending on your timing and size of your inputs the pendulum will remain almost stationary or it will start to swing.
As long as your push & pull and the movement of the pendulum is more or less in phase (swings towards you as you pull and away as you push) everything stays neat and controllable: Kick back. A very common phenomenon encountered when riding through potholes and over bumps, even in sand.
Next you move your input out of phase. Push towards the pendulum as it approaches you and pull as it moves away. If you get the frequency right the pendulum will swing madly. This is called resonance. Transferred back onto your bike: A tank slapper.
Now you have learnt:
The tank slapper is caused by a bump or series of bumps in the road. (One bump very rarely does it).
The damping of the steering has an influence: Front suspension geometry (rake, trail, steering angle, tire diameter and width) and mass.
The damping of the tire has an influence
Final conclusion:
Every bike may tank slap if the right (wrong) conditions come together.
Correct suspension setup and tire pressure does a lot to avoid tank slappers and is the most important cure.
Different type of tires can improve the bike but can also make things worse.
A steering damper can improve a problematic bike but comes with disadvantages. It should ideally act as an ideal (brick wall) low pass filter damping only the resonance of the steering (and above) but have no damping at slower movements. Existing dampers are unfortunately real world ones. Further disadvantages are added complexity and price.