I've only had to send out a rescue call once... I was riding gravel on my hybrid, riding fast to get back home before I totally lost daylight. I went down a hill and hit something like a big rock or pothole (the road wasn't the best at that spot) that I didn't see, and heard the hissing coming from my front tire. Instant pinch flat. Since it was at dusk and would take me a few precious minutes to change out the tube and I didn't want to try to navigate the last few miles of gravel in the dark since I didn't have a very good headlight, I called my wife to pick me up.
Tube ended up having not one, but two snakebites. Now when I ride gravel, I ride my mountain bike with bigger tires.