Algerian-born Yousaf Tarfasi, 31, was arrested in November on suspicion of raping the Sheffield Hallam student but was later released without charge.
Detective Constable Joanna Graves told the court that Tarfasi had always denied being the person in the CCTV or in the taxi despite officers being sure it was him.
On Wednesday, he was reassured by Mr Dorries that he was not on trial and that no-one was accusing him of any offence.
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The coroner said: “Were you the person who was with Caroline?”
He said: “Yes.”
Mr Tarfasi said he had been at a salsa club that night and added: “I was going back home and I ran across her and she was drunk and she was crying.”
Speaking through an Arabic interpreter, he said: “I asked her why she was crying and she said her friends had left her and didn’t want to go back with her to her house.”
Mr Tarfasi, told the court how he held her hand and they walked together to where she said she lived, at one point getting a taxi.
Asked directly by the coroner, he denied having sex with Miss Everest.
He said: “No. She was drunk and I helped her. She had no money. I paid the taxi then I left.”
He said he had given her his jumper and retrieved it from her before they parted.
Asked why he told a ‘pack of lies’ to police, Mr Tarfasi said: “I thought they were charging me with killing her.”
After giving his evidence, Miss Everest’s father, Chris, said to him: “Thank you for changing your story.”
Her family, from Walkey said how Sheffield Wednesday fan Miss Everest had a life-long love of dance and decided to stay in her home city of Sheffield when she chose to go to university so she could continue with her dancing and many other interests.