Flat tires are kind of not a big deal in sand, and actually do a better job of finding some grip in the loose stuff.

Standard operating procedure is to intentionally deflate tires for sandy terrain... fully inflated all-seasons tend to just spin.

I own a desert cabin on an unpaved road, and once drove the ~12 miles from town with a flat by deliberately keeping the flat side in the soft sandy shoulder for the entire pavement portion (~11 miles) of the trip. There was very little drama, and the wheel with the flat only got its paint scuffed up by the sand. Of course I drove slow to not beat up the bodywork with tire carcass, but it was perfectly mobile despite being a drive wheel on an open diff.

But WRT to ze Germans, they presumably got flats after making the idiotic choice to drive off-road in a rugged desert terrain in an unprepared minivan. Don't do that.