Speaking as a park ranger and an EMT (and also a National Mountain Bike Patroller), all trails, paved or unpaved, should allow exceptions for emergency situations. Our community recently built a corridor trail linking the two largest cities in the county, and although it is specifically designed to keep ATVs and snowmobiles (as well as cars and trucks) off the trail, the barriers are removable in an emergency. The local fire departments and sheriff's rescue squad have ATVs set up for patient transport. The biggest issue with modern ambulances is their width. (No pun intended.) Most paved and gravel trails are 8 to 10 feet wide. So are most modular (box-style) ambulances.
A few years back, we had a rider thrown from a horse deep inside our park, with had a possible broken back. Our trails are all 8-foot wide gravel/natural surface. The duty ranger and the local fire department used ATVs to access her and transport her out to the waiting ambulance. I think most, if not all communities have plans for this kind of occurance when trails are built. There would probably be major liability issues if they did not do so.