You were asking about "statistical studies"? I don't have them handy, but I did find some notes I made:
YOSAR did a study in 2013, that study pointed to;
Of the 2348 SAR missions,
Day-hiking, 1,379 SARs (588 injuries and 27 fatalities)
Backpacking produced 490 SARs (238 injuries, and 10 fatalities)
They don't break it down as much as I do (4 categories instead of 2), but it still supports my claims. The day hiking number is pretty SOLID, but the "backpacking" number needs to be parsed out further into distance hiking and bushwhacking.