I hae searched for, and found on numerous occasions,various lost individuals. I don't recall that any that we found were carrying a map or compass. This includes one park ranger who went out to check the nature trail 40 years ago and hasn't been seen since (probably met foul play, in my opinion).

A lot of factors may be involved in a "lost" incident, but I'll bet a decent map forestalls many searches....(either paper or digital).