The Theravada term came shortly after the Third Council. At the time of the Third Council, the early Buddhists were called something like 'Vibhajjavadins.'
The quote from Narada (or Bhikkhu Bodhi) is the classical view. There is also a 'Modern Theravada' view which focuses on the earliest teachings, such as the five Nikayas and the Patimokkha of the Vinaya. Just as in Asian countries there are many different forms of Theravada and some nations even have their own version of the Tipitaka (Burma) and their own patriarch, in many modern nations, we have been mostly arranged by the 'classical' view you quoted above and the 'modern Theravada' which may not see the Abhidhamma and the Commentaries as Buddhavacana.
I do not support litmus tests on what makes a Theravadin. It is very hard to get two people, even if they are married to agree on everything, I can't imagine getting all Theravadins to agree on the Abhidhamma and other issues.