But... I must say that I always thought "well rounded musician" to have a dual defined concept.
1- A musician that has an extensive knowledge of his/her instrument and it's capabilities. Which I guess is kinda what you were saying.
2- A musician that has the ability to perform in multiple genres of music.
Both of the points were captured in my prior definition. For point #1, a broad mix of instrument-related competencies and musicianship knowledge and skills. For point #2, a broad mix of repertoire and performance experiences.
Not just that, having the experience to play other instruments can also broaden a musicians palette.
As a bassist, guitarist and trumpeter, I definitely concur!