My kids were in private schools for years - it's definitely a bottomless pit. And sometimes you feel that if you don't donate, your children might pay the price indirectly (i.e., not get picked for awards, sports teams, etc.).
If you're committed to the school then I would try to get involved in a leadership position. That way you can influence the decision making, have some input, etc.
Private schools are hurting terribly in this economy, so you might have more "leverage" than you think (to effect change). And I would bet that you are not the only parent feeling that way.
We homeschool now, and it's a great feeling to use those tuition dollars in a much more efficient and effective way (and it doesn't cost nearly as much). Just think - that is "after-tax" money!
Good luck and I wish you the best.
PS: I would bring up that mom's story to the headmaster or principal and ask if it's true, and if so - why are they always asking for money?