That's not true, at least in the western US. Source: Me. 12 years running SAR missions in the western US. In CA and western mountain states, SAR rescues are free whether you are on federal, state or even private land. They are conducted by county sheriff SAR teams, state and federal rangers, and various military national guard units (and coast guard).

There are VERY rare exceptions for persons committing major felonies at the time. You will likely incur medical bills once handed off to private medical providers as you would if you suffered an injury at home.