Is it based on a true story?

Tldr at the bottom.
Brokeback mountain, despite it’s name sounding like a biopic on miners who were breaking their backs in kentucky during the industrial revolution, is a movie about two blokes breaking their backs doing something more kinky. Something even more kinky than mining? Woah!
It’s the movie found in the locked vaults of every homophobic republican.
And it’s the movie you should definitely watch with your family, if your family is a blind cat and a deaf dog, because any more family members mean a certain death from awkward tension, which is a leading cause of temporary paralysis in most teenagers.

But is it based on a true story? That’s a huge claim. It could be based on a book, which is based on the writer’s interpretation of true events. But she could be wrong, or lying. Calling it true because some writer said it’s true leaves us open to liability.
And even if she isn’t lying, who can say what is true in our universe? For all we know we live in a simulation running in a cosmic laptop which will run out of battery if we don’t all simultaneously yell “battery low please charge”. But humans lack that kind of coordination which means we’re doomed to die, along with our laptop’s battery.
All the existential crisis aside, Jake Gyllenhaal is an amazing actor, and a royalty(I’ve heard he’s a prince in the kingdom of Persia, but I haven’t googled this so don’t take my word for it). His new movie, The Guilty, which I’m the guilty of loving is the latest proof of his talent, and rightly earned royalty.
The other actor in the movie is the late Heath Ledger, the first guy to win an Oscar for portraying a comic-book character, and the best thing to happen to comic book movies since god said “let there be light”. Where god was probably watching the dark knight himself and by light he meant turn the brightness up so he can enjoy Heath’s performance on the cosmic laptop. Probably. I guess.
But were these two hunks portraying real people or really fictional people?
Well.. it’s the latter.
Brokeback mountain is actually based on a story that shares the same name, and was part of a collection which was a finalist for 2000’s Pulitzer prize for fiction. That settles it, it’s fiction.
Although Brokeback might as well be based on real life since it took till 2003 to decriminalize same sex relationships in the US, which is about 5 years after I was born. I’m not implying my birth is the reason they decriminalized it, I didn’t wield that kind of power when I was 5, like I don’t right now.
Anyway, criminalized or not, hate crimes against minorities are all too common, and I’m glad two of the best actors of our generation got to portray that in an Oscar winning movie. So kiss your friend today, on the lips, if you’re into it, it’s not illegal anymore. That’s the message you should take from that movie. Kiss your friends, and have children with other women, if you want to look as hot as Ledger.

Tl;dr
No it isn’t based on a story, because of some glaring plot holes, like the fact that no one in their right mind would hurt someone who looks like Jake Gyllenhaal, and that if it were to ever happen that people looking like Heath Ledger and Jake Gyllenhaal made out our reality would implode in itself because it’ll get too hot.