How can they assume this will not change how everything else works?

Yes. You can say statistically we did the comparison by holding everything else the same, but it only means "statistically". It definitely does not mean in reality you can hold everything else the same. There is no way when the policy changes, the system still works as before. This kind of study is totally delusional.

A policy works in other countries does not guarantee it will work in the U.S. For one thing, U.S. doctors make much more money than other countries. There are also other many differences. How can you assume you can simply move a policy successfully from other countries without making other important changes?