Advil has also been responsible for a several people I know passing very disconcerting amounts of blood. Those drugs may not cause stomach bleeding, but they seem to create truly dramatic amounts of blood release from the bowel. If i had only heard one story, but it's happened to quite a few people, including my doctor's mother.
I try to stay away from aspirin because of all the scary stories from increased risk of hemorrhage/bleed-out after an accident, to pancreatic cancer. Of course maybe none of those stories are true...