There was a case in SE Michigan about 15 years ago. A teenage boy was found tied to a tree. His story was that he and his girlfriend were in the park when they were accosted by a stranger with a gun. The stranger tied the teenager up, and abducted the girl. She was never found.
The teenager wasn't quite 18 years old, so the media did not release his name, but it was obvious that the police considered the teenager responsible, even though they lacked enough evidence to arrest him.
They thought he tied himself to a tree?
Yes, they did.
There was another case in Michigan about 15 years ago. Woman had been abducted from a Bar/Restaurant about a mile from where I live. She was raped and dumped back at the parking lot where she had been abducted from the next morning.
The next day, there is an update: the alleged rapist contacted the police. "I didn't rape her! It was a pickup from the bar, and I drove her back to her car. She even made me breakfast, and I have her fingerprints all over my kitchen."
Then the Bar maintenance guy comes forward. He had just been coming in to work when the woman was returned to the bar. The janitor said, "She was hugging and kissing him, and thanking him for a great night."
Come to find out the woman was married and her husband was out of town. She decided to have a good time, and came home to find her husband there, 4 days early, and she made the story up.
That one didn't give me chills: it made me so angry that I was seeing red. All the women who have been brutally raped and used who had their charges ignored because "the woman just makes it up," and this idiot did it.