I disagree. It is easy to experience by yourself. Practice unbalancing with first time beginner, and put him on the tatami. Nobody will regain 'naturally' his balance. They are collapsing and crashing on the mat.
And if your technique doesn't cause them to fall down, what do they do if you say nothing?
Even if it does cause them to fall down, what do they do next, without being prompted?
Would it be fair to describe that, if not injured, 100% of them will return to whatever perception of appropriate posture and balance that they have?
When you simply push an untrained person, even with a skillful vector that might result in a fall, after receiving the initial push (ukemi), what happens in their body, whether they fall or manage to remain upright? How do their muscles react? Is there variation? Is it predictable? Is it natural or unnatural?
In fact there is no universal definition of 'doing natural movement'. So it is useless to use it here.
I agree, without a shared definition it's difficult to have a discussion. But without an understanding of how human beings naturally (in their variations) interact with gravity all you have is some pretty dancing wherein both partners are required to do their part.
Start with a child learning to walk and observe their neuro-muscular behavior and how they deal with balance and movement in their learning process and you have a good starting place. Extend
A child can learn a lot of bad habits from the beginning, but it is clearly a natural process for a human being to attempt to recover their balance and posture (even a poor one) immediately upon losing it.
The model of ukemi that does not include that process as uke receives force is flawed, IME. Too many models teach uke to give up their posture (and often balance) in order to maintain their connection a 'look' a certain way.