Longshot is not based on a true story. It's a work of fiction that was developed to engage and captivate the audience through an invented narrative and fictional characters.
Madden Longshot isn't based on a true story. It's a concoction of imaginative elements put together to captivate players. There's no real-life basis for the plot or the characters in it.
It's not clear which specific 'Caine' is being referred to here. It could be the character from 'Kung Fu' or some sort of made - up or less - known reference to a character in the world of 'Pulp Fiction' that has some connection to the idea of 'Caine' from 'Kung Fu'.
Overall, Trigun Stampede adheres closely to the manga. Some minor details might differ for the sake of the adaptation's flow and visual presentation, but the core remains the same.