Well, I have had flats offroad before. One time, I got a flat tire, so I pulled over. When I was pulling over, another tire failed. Since then, I have been running two spares, and I have yet to have a tire fail.
Breaking a bead is easy and reseating a bead is not too bad either (as long as you have a sufficient air supply). However, the labor and equipment involved in dismounting / remounting a tire on a rim in the boonies is not worth it. Buying good tires and carrying two spares is all you'll ever need - unless you really are going to the Amazon.