Thanks for the rules @ Jens K A. The scenario you propose is very interesting as well and I'll be happy to know the official answer (although if it's unlikely that they answer you).
However, I've been musing on it myself and I think you could be wrong.
On page 178 they said:"If three (3) players each have one (1) win, a player having played less than all three (3) matches is automatically
eliminated and the player advancing to the single elimination
competition is the winner of the match-up of the two
(2) players tied with 1-2 records".
It's therefore possible that the three-way tie rules apply only in a situation where 3 contestants have only one win each. I've saw nothing about your scenario, in which 3 players have 2 wins and a loss. Logic would dictate that Caroline is actually not tied with her opponents, since she'll have a positive H2H against them.
In any case, that's an interesting suject of reflection. Decidedly, the Round Robin is full of mysteries