Some of the local, free-standing psychiatric hospitals also these centralized "bed management systems" as the same physician will be doing doc-to-docs for multiple hospitals at the same time.
At hospitals that I've worked at and hospitals that I've transferred patients to, in general the role of the physician is generally to ensure that the patient is medically stable and that any pertinent issues with respect to medical comorbidities are being effectively managed. Issues related to ensuring that staff can manage the patient, insurance authorization, etc. are handled by other staff.
At the unit that I work on, the nurse has already reviewed the patient's clinicals, verified insurance, and done a nurse-to-nurse before we're even paged about the patient. Consequently, our job is to essentially ensure that nothing is being missed medically and that there are no other big issues that would be exclusionary for the unit that somehow got missed. It'd be extremely unusual for one of the physicians to refuse an admission/transfer at that point. Then again, our nurses are pretty good about screening patients, so I'm sure there some folks that are refused that the physician staff isn't even aware of.