Presumably they also went to non-Jewish doctors if they had a medical emergency on the Sabbath.

Nitpick: Jewish law permits and in fact requires the breaking of Biblical commandments if someone's life is in danger (exceptions: idolatry, murder and breaking sexual taboos). In fact, there's an old Jewish joke that I think gets at some of the moral weirdness you're bringing up here:

A Jew and his Christian friend are sitting down for dinner at a restaurant. The Christian recommends the cheeseburger, but the Jew says that, since he keeps kosher, he's forbidden from eating any meal with both meat and dairy.

The Christian asks whether the Jew would eat a cheeseburger if his life depended on it, and the Jew says that Jewish law allows someone to break a ritual law if zir life is in danger. So the Christian draws a handgun, points it at his Jewish friend, and says "Order the cheeseburger, or I'll shoot!"

After dinner, the Christian puts his gun away and apologizes to the Jew. "You know I never would have shot you," he says. "I just wanted to see what you would do. Please forgive me."

"Forgive you?!" asks the Jew. "Of course I won't forgive you! Why didn't you make me order the bacon burger?"

In conclusion, if your morals make you wish someone would come along at gunpoint and force you to break your moral system, you may also be in error :)