by sdiberar
The key is the second sentence of 7.1:"Otherwise, whenever any player does so [...]"
This means, if any player (or more than one player, by the usual definition of "any") passes a victory check, then [continuing the sentence in 7.1] "[...] the Faction that reached the highest victory margin (7.3) comes in 1st place[.]"
So long as at least one player passes their victory check, the highest margin wins.