They have hundreds of MOAs that make both entities, at least from an in-patient/surgical perspective, unseverable. Could they survive without each other? Kinda sorta, not really. The co-dependency amongst pick-a-product-line is essentially what makes them one in the same. Also, DoD (Army mainly) has an important presence in Trauma with both Jackson and UHealth to maintain proficiency and medical readiness (AF uses Baltimore Shock and Navy uses Tulane Trauma... I digress).
Also, most UHealth outpatient refers specialty care to Jackson campus, in turn, in-patient admissions go from UHealth to Jackson. Then for rehab stints, Jackson releases back to UHealth because its all one giant campus with the outpatient feeder clinics extending their reach farther and farther afield.
Its brilliant actually.
Yes, Baptist pursuing a Trauma Center (I heard it was going to start as Level III) is laughable and the Certificate of Need was denied rightly so.