Reb Dovid,
If all else is well between the two of you and this is the only real issue, I wouldn’t think it’s wise to drop the shidduch because of it.
It depends on what kind of rav you want him to be, but if he’s involved with her, she needs to be comfortable with him. I doubt she’ll care if he is only paskening shailos about kashrus and the like, but if it’s anything more personal or hashkafic, SHE needs to feel comfortable with him.
I actually think she handled it pretty well. She is not telling you that YOU have to in any way limit your sheichus to him. She is telling you that she is not comfortable having him as her mentor.
For the record, don’t rely on anyone to make the decision for you. Not this rav. Not any other Rav. Make sure you have the spine to make your own decisions.