True Story?

[deleted]

Although I don't know this for a fact, I can pretty much guarantee that when they say "true story" they're simply talking about the fact that the idea came from a real life incident of someone getting their head chopped off by a guard rail, not that some women really kept her boyfriend's head in the fridge like that.
For one thing if that really did happen they would certainly have made a bigger deal about that fact while advertising the movie and might even have sited real names and specific locations, it could only help sales (probably by a LOT) and we'd probably all be familiar for the story right now, like Psycho and Chainsaw Massacre did for Ed Gein. But since it was only inspired by a common accident they wouldn't want to make too much of a ruckus about it being "true" less the truth might disappoint potential viewers, it would be better to just to let their imaginations wander.

Also I think it's HIGHLY unlikely that a woman, no matter crazy she was, would be able to hide the head and keep it from investigators. Even if it clearly was an accident they're not going to like the idea of the head missing, for one thing it makes them look incompetent, second no doubt the man's next of kin wouldn't be happy about it unless there was a very good explaination, and third they wouldn't want to take the chance of some innocent person or kid stumbling upon it later. Also it would beg the question as to whether there was a bit more to the "accident" than it appeared, such as the victim having been shot or hit with something and knocked unconcious before the crash, and then the passenger trying to cover that up by hiding the head which conveniently had been severed, and that would lead them to take a much closer look at them.

Regardless they likely wouldn't let the matter rest until they were certain where it went or at least the scene provided a logical explaination for it being gone, such as it happening in or right next to a river. Also, where would she put it? Purse? Glove box? They would certainly check the truck once they determined that someone must have moved it.

I'm not saying it's impossible, there are certainly other cases of people keeping dead bodies of loved ones around, but with the circumstances they show it just seems very very unlikely.