What is the most widely believed though likely false aspect of the olympic truce story

The truce ended all wars

Explanation:

The Olympic Truce or the sacred truce, is the declaration made by ambassadors for the laying down of arms and the stop of all hostilities starting from seven days before the  Olympic games began and ending seven days after the games to provide safe passage for travelling athletes and also spectators to and from the Olympic games

However, the  games were held during Persian wars and also during the Peloponnesian wars. As such the truce stopped mainly conflicts that have direct impact on the Olympic games and there was an attack in Olympia in 364 BC during the games.