That claim appears to contradict the second-system effect [0].

The observation is that second implementation of a successful system is often much less successful, overengineered, and bloated, due to programmer overconfidence.

On the other hand, I am unsure of how frequently the second-system effect occurs or the scenarios in which it occurs either. Perhaps it is less of a concern when disciplined developers are simply doing rewrites, rather than feature additions. I don't know.

[0] https://en.wikipedia.org/wiki/Second-system_effect

I won't say the second-system effect doesn't exist, but I wouldn't say it applies every single time either. There's too many variables. Sometimes a rewrite is just a rewrite. Sometimes the level of bloat or feature-creep is tiny. Sometimes the old code was so bad that the rewrite fully offsets any bloat.

The second system effect isn't that a rewrite necessarily has more bugs/problems. The second system effect is that a follow-on project with all of everybody's dreamed-of bells and whistles that everybody in marketing wants is going to have more problems/bugs, and may not even be finishable at all.