[steven]

"We say 鳥が鳴く all the time without knowing which particular bird it is that is singing."
This example would reside in #2 on the list in the grammar book I took a look at. It's like something that you've noticed and you want to exclaim it (which is something done in Japanese more often than English by the way).

It's interesting because it does kind of contradict the idea of "主語の選択を表す"こと. Again though, it's kind of an unrealistic example to say "it is the bird that's singing" (as opposed to a bell, whistle, other animal, etc.), so I agree with Sashimister 100% on this.

By the way, chiuchimu, are you Japanese-American? I know that some words are used differently by Japanese Americans, so maybe that explains the クラスは/が example. I know there are a lot of Japanese American specific phrases/words that Native Japanese wouldn't use. (like 試験をとる instead of 受ける and the like).