Did I handle this professionally?

Hi everyone, I started working at a local hospital about 2 months ago. It’s my first clinical job so I’m still learning. The hospital has around 4 -5 doctors on staff, some are older (70+) and the others are younger (~30s).

Yesterday I was the assistant/tech for one of our older doctors. The owner didn’t agree with the doctor’s opinion, said she would seek a second opinion elsewhere. When I went back in without Dr. to go over meds, I informed her if she wanted a second opinion, she could always call the front desk and request to be seen by a different doctor in the future. O said she “did not like” the Dr. she saw yesterday and asked if we “get that complaint a lot”. Obviously I’m not going to talk badly about any of our doctors to a client, but I didn’t really know how to respond at first. My response was pretty much, it depends on the person. I told O that some clients prefer our younger doctors, and others prefer our older doctors. I said I understood why she may have felt that way and advised her to seek a second opinion within our hospital.

Is this the professional/respectful way to handle situations like this? Any advice for dealing with disagreeable clients in the future? I hadn’t encountered a room like that yet so thought I’d ask here. TIA!!