I'm not sure why so many people here think this is a good idea and are suggesting it.
There's just so much badness that can come from commenting about other practices to clients while on the job. It's absolutely deplorable to make negative comments. Even if clients themselves make negative comments about another clinic, it's not okay to chime in and add fuel to the fire. You just say I'm sorry you felt that way or I'm sorry you had a bad experience or something without agreeing and move on and redirect. It's just as bad if not worse to put your hospital in a negative light.
You are not really hired to please the clients/patients through your own moral compass or drum beat or whatever. You are hired to help clients/patients as an agent of your employer. The clients/patients "belong" to the hospital. I know that sounds weird but that is why noncompetes/nonsolicitation clauses are such a big deal. You cannot do anything purposely to sever that relationship between client and hospital. This is a really important concept to understand. It's similar to the idea that you have to understand money and payment ARE important in this business. Your job is to promote your hospital. If you are uncomfortable with that, then you should probably move to another hospital that you feel comfortable recommending.
If a client asks you what other local hospital you recommend because they would like to leave, the correct answer is, "oh no, can you tell me what it is that you were unhappy about? Is there anything we can do to provide a better experience?" NOT, "I've heard great things about practice X, and I used to work at practice Y, etc..."
If the client says, I just really don't like Dr. Z, then say you're sorry s/he feels that way. If Dr. Z's the only doctor there, then just wish them well and move on (if my techs heard this, they would say something along the lines of "I'm sorry you feel this way. I personally really love dr. Minnerbelle and think she's a great doctor.") If I were Dr. Z, I personally would want to know. Either I will learn something from the experience, or I'll jump for joy that we're ridding ourselves of dingus client.
I say all of this as an associate with no real stakes in the hospital. The only time I recommend elsewhere is for people who are low income enough to get government assistance, who would qualify for subsidized care and they have a pet that really needs care they can't afford.