In almost any implementation you don't want to track the owner because it is only an unnecessary overhead and nothing else.

On a similar note the articles strikes me as somewhat contrived example, because the most obvious implementation of reentrant mutex also does not care about the owner thread.

Edit: Another reason why it feel contrived is that in fact reentrant mutex represented as first class datastructure (in contrast to monitor as an language-level construct) is to some extent only an hack to solve issues stemming from improper design.