In February, a group of cardiologists in Gainesville, Ga., announced they were building a diagnostic heart center in an $18 million joint venture with the local hospital. Last month, they said the project was dead. The reason? Federal Medicare officials want to crack down on arrangements like the one that was planned in Gainesville, where doctors refer patients to businesses in which they have a financial stake. In recent years, many physicians have become wealthy by investing in magnetic resonance imaging, or MRI, facilities, surgery centers and diagnostic sites -- and then sending their patients to them. A recent McKinsey...