Not an absolute truth, I'd say.
It highly depends on the car and course, for example the '04 Pescarolo has such a high fuel consumption compared to tyre wear that R1 tyres are useless, the car will run out of gas long before the tyres go out. If I recall correctly it could run with R3 in the front and R2 in the rear, and only then wear the tyres out before the tank was empty.