Did this statistic control for how people select certain hospitals (where applicable)?

Obviously, if a hospital is specializing in C-sections, it will handle cases where the likelihood of having a sectino is much higher.

(Similarly, hospitals are very dangerous places if you compare the death rate in a hospital to the death rate at any other place where people stay. Of course it's mostly not because hospitals kill people, it's mostly because people go to hospital when they are sick.)