The idea of settling a chess related dispute through playing a match goes a long way back, and at least has the befit of being less violent than actually shooting at each other. Indeed there seems to be a current dispute in Australian chess involving this conflict resolution, although it seems the lower rated player is not so keen on accepting the challenge (Noting that some point the past the same player had challenged other, lower rated players to matches in a similar way!).
Of course the risk is that it actually doesn't settle much, as shown by an old joke I found in "Chess with the Masters" by Martin Behim.
Burletzki (a coffee house player) arranged a 6 game match with a German master named Kohlein. Kohlein one the first game. Burletzki said "I made a silly mistake". Kohlein won the 2nd game. "You can't be expected to win every game". Kohlein won game 3. "I'm not in form today". Kohlein made it 4 in a row. "He's not a bad player". Kohlein picked up win number 5. "I think I underestimated my opponent". And after Kohlein won game 6, Burletzki admitted "I believe the man may well be my equal"
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