Yes, FMC and Davita are the largest - but there are many others out there. I travel once or twice a year and have had treatments at these other facilities (at least these are the different one that I can remember)...
DSI
Liberty Dialysis
A couple of hospitals that had out-patient in-center HD
US Renal
Dialyspa
DSI was purchased by DaVita; Liberty was purchased by FMC. Most hospitals have spun off their outpatient operations to either DaVita or FMC, who provde dialysis to about 70% of the market, which means there about 1,500 non DaVita/FMC units but they are getting harder to find. DCI out of Nashville is the third largest provider and the largest nonprofit. DCI is about 1/10th the size of DaVita.