The court heard the woman said she thought Grey was a good Samaritan when he stopped to help her and her fiance after they crashed in Fairview Downs about 9.30pm that night.
She and her partner were arguing and she thought Grey, who is profoundly deaf and needs a sign language interpreter in court, offered her a ride home.
Guthrie said a time stamp from a nearby service station showed Grey's red Ford Mondeo leaving the scene at 9.50pm. He went to an ASB money machine in Five Crossroads and withdrew $20 at 9.59pm as the woman waited in the car.
He then took her back to his sleepout at a property he was living at, allegedly striking the woman on the face when she tried to escape the car after realising they were heading away from her Hamilton East address.
Guthrie said the woman's story was that man dragged her by the arm to the sleepout and once inside pushed her on the bed with force, pulled off her pants and raped her as she struggled and called out repeatedly for him to stop.
She then fled when he left the room and ran to a busy road where she flagged down a car with two women.
Those witnesses said it was 10.20pm when they picked up the woman and that she was crying, frightened and yelling "He's after me".
Grey was seen near the crash scene in his car shortly after by another witness and was recorded buying McDonalds at Five Crossroads at 10.43pm.
The two women took the alleged victim home at 11pm and the police arrived at 11.10pm. She underwent a medical exam at 3am which showed evidence of sex and injuries to her upper body including bruising and scratches.
Grey's story was that the pair had "rough, messy sex", that the woman's advances initially made him sick and feel cheap and used, that she "begged" for sex and he eventually thought "Oh well, why not? She wanted to".
Defence lawyer Jared Bell said Grey did not have to prove his innocence, that it was up to the Crown to prove the charges against Grey.
He said the first charge of abduction could not be proven because the victim willingly went with Grey in his car.
In relation to the charge of rape Bell said the jury of six men and six women needed to question how credible and reliable the woman's testimony was given she was drunk, she had driven drunk, she was emotional after an argument with her partner and she changed her story by first telling witnesses a man "tried to" rape her.
He said the jury had to consider whether the woman made the claim after regretting consensual sex and that the defendant did not know how the woman got her injuries.
Bell also asked the jury to make allowances for Grey's hearing disability because communication was difficult on the night.
The jury is now deliberating.