Is there any evidence for these assertions?
Wouldn't it make intuitive sense for "writing new code to do a task" and "tracking down a problem debugging code" to be multiple different skills and not the one same skill? Wouldn't it make sense for the one you do more of to be the one you are better at, and not directly 'smart' related? Wouldn't it make sense if tooling could affect the ease of debugging?
"Understanding what code is doing" is a unitary skill (even if it has many different aspects to it, along with language and task specific details). There are plenty of people who are good (enough) at writing new code to do a task but do not understand how to debug; there is (I would suggest) nobody who is good at debugging code who is not also good at writing it.
The evidence is that many respected people with decades of experience generally agree with them. They are not scientific theories that require validating through testing, they are general advice that is usually true and good to keep in mind.