The 'rule' doesn't properly cover subtleties.
He spoke passionately about the importance of using empathy while
still maintaining a position of clinical neutrality.
is actually ambiguous, but the default reading corresponds to the one you indicate. 'His' topic was The importance of using empathy while
still maintaining a position of clinical neutrality.
However, with the addition of the comma,
He spoke passionately about the importance of using empathy, while
still maintaining a position of clinical neutrality.
means
While still maintaining a position of clinical neutrality, he spoke passionately about the importance of using empathy.
In none of these is the 'whereas' sense in play.
In your example, only the 'What came to my mind was The importance of using empathy while still maintaining a position of clinical neutrality' reading makes sense, so the comma should be omitted.