Point 6. Read carefully all Travel insurance exclusions. I know people that were not covered by Travel medical insurance because the accident happened under a circumstance not covered by the travel insurance policy (e.g. many "extreme" sports are usually not covered! the clearest example is Skiing which is not covered by many EU travel insurance policies, except if you buy a specific coverage for an extra.) Antoher example: if you drive a motorbike >100 cc.

Furthermore consider that often some Insurance companies provide stand-by payment procedure: first you pay then they reimburse you, except if amount is particularly high where they usually provide direct payment. In particular when you have the right to choose the hospital (choice that frankly I consider essential!)