Looking for a reference about the significance of The Buddha being a teacher
No idea who the author you are talking about is, but what he/she's referring to is a samyaksambuddha.  It's canonical at least from a Mahayana perspective.  A samyaksambuddha is a once in a kalpa being.  He (and it's always been a &quot;he&quot; in this world system) is a Buddha without karmic remainder.  He is fully awakened in terms of his own existential obstacles and his investigation into reality.  He's also perfected all of the paramitas, mastered all of the dhyanas, and so on and so forth.  And yes, like you indicate his ability to teach is of paramount importance.
All being a lowercase &quot;buddha&quot; means is someone who has awakened.  If you want to bring the Theravada into this, a buddha is anyone from a sotapanna to an arhat.  The title capital B Buddha explicitly refers to someone who is a perfected Bodhisattva who has mastered all aspects of the path.  He is the person who restarts the sasana after it has been lost.