She did not see Mr Frost, and as she turned in front of him he hit the right side of her car.
While she accepted responsibility, she accused Mr Frost of causing further damage to the car by throwing his bike at it in anger after the crash.
IAG was seeking $1273.44 from Mr Frost for that damage.
But last night, after inquiries from the Herald, IAG spokesman Craig Dowling said the case would not be pursued in court.
He said the owner of the car backed out of the hearing within hours of the Herald contacting IAG.
Mr Frost was relieved, but said he would be taking his own legal action against the company and the driver.
"What they have cost me is ridiculous," he said. "I will definitely still pursue them. It's certainly not worth my time or money, but they have pushed me this far and pushed my buttons. I have to do something. It's become a matter of principle now."
Mr Frost was injured while cycling to the gym from his Westmere home on November 23.
"The lady passed me in her car then swung around in a u-turn right in front of me. I hit her pretty hard and flew onto the bonnet."
He flew through the air and hit his head on concrete as he landed. In the seconds before he struck the ground, he wondered if he would survive the injuries he knew he was going to get.
Mr Frost said he did not remember anything for the next 10 minutes, and for hours after everything was "hazy".
He had no memory of throwing his bike, but said if he had it would have been the result of him being shocked that he had been hit combined with the head injury which resulted in confusion and concussion.
He received a letter from the NZI insurance company dated November 24, saying he "may be responsible for causing some of the damages".
"... you then picked your bike up and have thrown it ... causing damage to the bonnet and windscreen. Because of this, it will be our intention to hold you liable for the costs of the repairs ..." it said.
In March, IAG - an Australian company which owns NZI, AMI and State Insurance in New Zealand - contacted Mr Frost to tell him his actions were "malicious damage".
He was then notified the case would be heard by the Disputes Tribunal.
But last night the pin was pulled on the hearing.
"The update I have just received ... is that our insured, having received notification of the hearing, doesn't wish to pursue this through the Disputes Tribunal given the potential time and cost involved in appearing," Mr Dowling said.
He said "irrespective of the outcome" of the hearing, the company was comfortable that everything had been done correctly when it came to the claims procedure process.
Mr Frost was angry IAG had considered pursuing a victim, and said its accusation of "malicious damage" was scurrilous.
He intending seeking $3999 from the driver. This included $1599 for his "knackered" bike, legal costs and for damage to his helmet and sunglasses.
In a document he will file in court, he said the sum he was seeking after his "near death experience" also took into account the "sleepless nights and emotional distress that dragging this episode up again has caused me".
