I think this instinct may in fact be evolutionarily optimized for conflicts between individuals; in most group conflicts in the ancestral environment, you probably already belong to one of the sides.

But yes, it does seem to generalize too readily to conflicts where you personally wouldn't sway the balance.

EDIT: How could we test any of the above theories? My theory seems to predict that describing the conflict as "one single entity versus another" (and triggering modes of thought optimized for third parties to single combat) will give a stronger underdog bias than describing a collection of entities on each side (with one collection much larger than the other).