A physician, including psychiatrists, have an unrestricted license to practice medicine. It's unrestricted in terms of time, location, and scope of practice. Granted, they will be held to the standard of the specialty they're practicing (i.e. if the psychiatrist decided to do a heart transplant, they'd be held to the standards of a transplant surgeon), but there's nothing legally wrong with a psychiatrist taking over patient care on an ambulance.
Also medical school and the first year of residency ("internship" year) are inherently general education. It's not like the psychiatrist wasn't educated in non-psych diseases and disorders and spent all 3 years of his/her psychiatry residency working with psychiatric patients.