Can the doctor refuse to give my daughter a referral of her choice?

She has to have gall bladder surgery. She was originally set up with a Doctor B to do the surgery at South Central Regional Medical Center, which is a local hospital. However, this county is notorious for killing people. The most recent example, a friend of hers, in her late 20’s, otherwise healthy, died about a month ago from septic shock after surgery here. She found out that Doctor B was the one who performed the surgery. (Again, this is not a rare occurrence.)
My daughter called her regular Dr., Dr. J to ask for a referral to Wichita. Apparently the customer service rep told her that Dr. J had already given her referral options.
Corrie said, “Yes, he gave me the choice of Dr. Sam, who I don’t like, and Dr. B, who I just found out did surgery on a friend of mine who died, so I want a referral to Wichita.”
She’s waiting to hear back. Can they deny her the referral because she wasn’t satisified with either of her options locally?