I know of several psychiatrists working on palliative medicine services who are not fellowship trained. you probably can't get away with this nowadays but in the past it was possible. TBH it is not terribly difficult to learn how to manage
btw there is a difference between a palliative care psychiatrist and a palliative medicine physician who has their basic training in psychiatry. Palliative care psychiatrists are essentially C/L psychiatrists, often with an interest in psycho-oncology and end-of-life issues. someone like susan block or scott irwin would be an archetypal example of a palliative care psychiatrist. essentially providing psychiatric consultation to patients with cancer or at the end-of-life or with other terminal diagnoses. common consultations would be demoralization, existential anxiety, refusal of treatment, capacity assessment, delirium, agitation. on the other hand a palliative medicine physician who happens to be trained in psychiatry would be working on a palliative medicine service in the same way as another physician from another background (and it's not just IM or FM, though those are most common). Consultations include referrals for hospice care, management of pain, nausea and vomiting, anxiety, agitation, constipation, diarrhea, confusion, breathlessness, providing psychosocial support, dealing with complex family systems issues. So yes a palliative medicine physician who happened to be a psychiatrist would have to manage the whole gamut of problems on a palliative care service that someone with another background would.
I think psychiatry provides a great background for palliative medicine since both specialties focus on symptom control and privilege psychosocial aspects of care, and the importance of multidisciplinary working, and there is an overlap with some of the consultations though the approaches differ and palliative medicine has a more more collaborative approach that psychiatry typical does.
I really loved palliative care but decided there was no way I could do it in this country where you are working against a system that will not accept death.