But I am not sure that there is a difference between musical rhythmic sense and rhythmic accuracy. To me it is a matter of semantics.
Both my dds take piano lessons. My oldest dd is very good technically (rhythmic accuracy) and her teacher raves about how quickly she progresses, but she has no musical rhythmic sense. She does not feel the music. She doesn't even enjoy music, but she like the intellectual challenge of learning to play the piano. My youngest dd has great musical rhythmic sense and even her beginner songs sound like music. I guess you could compare it to the difference between a computer playing a song versus a concert pianist playing the same song. The first would be more rhythmically accurate while the second would have more rhythmic sense. I suspect that most good musicians possess both.