Hmm, I now see that the tournament you played in is a counterexample:
That was created 12 days ago, so it's not as if were some very-old tournament.
It's a round-robin in which each game has a winner and a loser
The "Score difference" shown by clicking the plus is exactly what would be given by having all wins
be +1 and all losses be -1. In particular, the top 2 players have the same value for that column.
Furthermore, I have gone through a replay, and don't see any other indication of there being scores.
There are no players with 0 losses, and exactly 2 players with only 1 loss. In particular, one of those two
players lost to the other of those 2 players, and whoever won that game lost to a player who finished lower.
Thus, the two things from my previous post would break that tie in the same way.
However, BGA - for some reason - broke it in the opposite way.
You might try
https://boardgamearena.com/support , in case they will respond to this.
(I have gotten a quick response on something else, but I also seem to recall
seeing long-open threads on tournament tiebreaking that BGA has not answered.)
For
https://boardgamearena.com/support , I would do
GAMES & PLAYERS (this explicitly includes tournaments)
then
COMPETITION (again, explicitly includes tournaments)
then
I didn't get any ELO points after my game , since the 2 lower options do not have a
"My problem has not been solved" button, and this one seems closer than the 2 higher options
(it's not "didn't get ELO" , but it
is "didn't get 1st place" ,
in the tournament for which you were the administrator)
.