Steve and I observed a similar fight a few weeks back at Lake Pend
O'Reille. We don't know if there was a nest site though.

A difference between the fight Bill reported and the one we observed
is that as the two (presumed) males fought and the (presumed) female
watched, a fourth goose came in and swam away with the female. We
had to leave, so I don't know what the outcome was. (Narrow road,
big car blocking it, others wanted by, etc.)
jw
Jane Westervelt
Steve Kalloger
Moscow, ID