You can't survive or beat death: once you are dead, you can't go back! But you can "cheat" death, meaning you can get better after almost dying, or avoid being killed.
The rule for prepositions when you travel is that we say "on" when you can stand or walk inside the vehicle, and "in" when you have to sit inside it. So were are on a cruise ship, but in a rowboat; on a train but in a car. An ambulance is larger than a car, but we still can't walk inside it, so we use "in."