Technically probably correct but I think we're getting into semantics. My opinion for what it's worth, is the lowest note in a chord could be in a very high register. To me that doesn't make it a bass line. It's just below the other notes. Bass has to define a sonic register to me and that means low frequencies. Usually very low as in tuba, double bass, electric bass etc.What is a bass-line?
"A bass line is the lowest-pitched part of a piece of music, typically played on a bass instrument such as the double bass or bass guitar.
Bass lines can vary in style and complexity depending on the genre of music."
Of course those instruments can play higher but they usually don't.
For the purpose of specifics in describing music, low is a more general term whereas bass is to me, more specific so whatever the text books say I'm sticking with bass being very low frequency rather than just the lowest note in the chord which could in fact be way above middle C.
) extra notes while playing live. One of the reasons could be the player's insecurity (for this/that reason.)