Actually it's pretty well supported by data.
If it were well supported by the data I wouldn't have said that it keeps being repeated without any good evidence. In reality, all of these claims are only supported by the "research" of S.A. Marshall, and there's no evidence that the guy ever actually did the research that he claims he did. There's certainly no replication of his results. But there is evidence that he had a habit of making up data to support his narratives.
In fact, it's one of the reasons veteran units are so dangerous. Most of the members are actually trying to kill you instead of just shooting in your general direction.
This is like saying that the reason professional basketball teams are so good is because they actually try to score points. Silly, at best.
The actual reason veteran units are so dangerous is because:
1. They're experienced.
2. They're a (literal) example of the survivor bias; most of their crappy soldiers die off, shifting the bell-curve to the right.