Yes, in fact M has repeatedly told me that while she is "on my side" she does not all see J in a bad light and doesn't judge him or our conflicts. She is highly respectful of the relationship I have with J and has been very sensitive in both her words and actions in giving J and I the space we need to work our conflicts out. And, I think what she means by being "on my side" is an indication of her empathy to the conflicts J and I go through. (Although I could ask for clarification). She has never said anything derogatory about J or attempted to put a wedge between him and I. She has actually offered advice, feedback, and solutions and has acted more like an sounding board. I have not been concerned about any ulterior motives that she might have.
I agree that it may be beneficial for M and J to talk directly. I think it could be helpful for J to explain why the privacy violation hurt him, and for M to explain how she doesn't judge him in any way and for the two of them to reiterate their respect and like for one another.