Cecil says it only to refute it. The mechanically naïve see it as quite natural—just consider any popular legend involving scale, from Swift to “Honey, I Shrunk the Kids”.
A man who fell from the top of the Empire State Building. As he passed the 20th floor, he thought to himself “Well, so far, so good.”
On the other hand, if you land on your feet, you can use your leg muscles to slow down and absorb impact. And the key metric there is just how much muscle mass (or volume) there is to absorb energy.
As a proportion of body weight, children and adults have roughly the same amount of muscle (a little less for children, as their proportions are different, but it’s not a square-cube difference). So adults and children should both be able to successfully land on their feet from about the same height.
It’s the same analysis which says that, roughly, vertebrates of all sizes can jump to the same height (assuming they’re all proportioned the same). Jumping height is directly proportional to speed leaving the ground, which is jumping force x distance /body weight. Force is proportional to cross-sectional area of muscle (which is proportional to height squared), distance of acceleration is directly proportional to height and weight is proportional to height cubed. All the height’s cancel, and you get a constant jump distance for any given size.