That's not exactly true. Building or owning a hospital is not an issue. Referrals are the issue.
The original rules that dealt with physician ownership of hospitals are contained in the Ethics In Patient Referrals Act of 1992 (also called the "Stark Law"). Doctors can build a hospital, but if they refer patients for 'designated health services' at the hospital, they can't submit claims to Medicare or Medicaid for those services without violating the federal False Claims Act.
The Stark Law had exceptions for rural hospitals and specialty hospitals.
That's a little simplistic, but I hope you get my point.
You are correct about self referrals. However, many physician owned hospitals have luxury suites with real beds, gourmet meals and attentive nurses. They build a reputation for such care and there is no need for self referral when everyone in town wants to have that type of care. They do not scrimp on nursing care either. The largest hospital in our town has been plagued with infections and cut backs in nurses as well as support staff. They also cut the air conditioning in the summer months where we typically see temperatures in the 100 degree marks for weeks on end. Who wants to lay on a plastic mattress during that time??