Bitterness is quite literally the "this is poison, stop eating" taste category that incidentally happens to have a lot of false positives because for the most part it's cheaper to reject some good food than to accept eating some poison. An ironic thing to say in a thread about peppers, but still.
And much much more false negatives, which raises the question if the "stop eating this, this is bitter and bitter means poisonous" has any truth in it.
If bitter = poisonous, then the plants that evolve to be more bitter will be eaten less. Thus, non-poisonous foods that evolve to be more bitter have a genetic advantage over their less bitter counterparts.
That would be true if there were a fitness advantage for the plant when a herbivore dies, but in actually the fitness advantage comes from discouraging the herbivore from eating the plant.