About depressing/dark movies...I have a few in my collection that I always thought fit that category.
Sleepers - (1996) After a prank goes disastrously wrong, a group of boys are sent to a detention center where they are brutalized; over 10 years later, they get their chance for revenge.
Mystic River - (2003) With a childhood tragedy that overshadowed their lives, three men are reunited by circumstance when one loses a daughter.
This last one has some supernatural/religious overtones in it, it might fall a little under your "unbelievable" category but I recommend it none the less.
The Ninth Gate - (2000) A rare book dealer, while seeking out the last two copies of a demon text, gets drawn into a conspiracy with supernatural overtones.
Sleepers - (1996) After a prank goes disastrously wrong, a group of boys are sent to a detention center where they are brutalized; over 10 years later, they get their chance for revenge.
Mystic River - (2003) With a childhood tragedy that overshadowed their lives, three men are reunited by circumstance when one loses a daughter.
This last one has some supernatural/religious overtones in it, it might fall a little under your "unbelievable" category but I recommend it none the less.
The Ninth Gate - (2000) A rare book dealer, while seeking out the last two copies of a demon text, gets drawn into a conspiracy with supernatural overtones.