Your theory is not quite correct. While hikers are indeed one of the leading causes of SAR incidents, climbers are quite far down the list. Some of the best hard data I'm aware of comes out of Oregon. See: statistical Data for Oregon on the Oregon OEM site.

If you open Accumulated SAR Data 1997 to 2013, you will find an interesting graph on page 34. There you will see that the largest number of incidents are for "Hiking", followed closely by "Motor Vehicle", "Wandering", and "Hunting game". You have to go down to number 7 to find "Climbing", with "Mushroom picker" close behind.

The reason climbing is often perceived as a major source of SAR incidents is that climbing incidents tend to make better, more exciting, and more photogenic media stories. A story about helicopters plucking a climber off of a tiny ledge tends to get way more media coverage than a story about searchers slogging through the brush in the rain looking for a hunter who couldn't find his way back to camp. But the truth is that while climbing rescues can be spectacular stories, they actually make up a surprisingly small percentage of SAR activity.