To my knowledge there could not have been a claim without your daughter being fully aware of it. It is possible that the other driver had a reason not to claim , e.g driving while uninsured is a possibility. He could also have later reflected the damage was so minor that it was not worth bothering about. Most insurance companies I know of are not interested more than 3 years later in any previous claim. Acting in good faith it would be quite reasonable for your daughter to believe no claim had been made. I ( and I'm cautious ) wouldn't think there had been a claim and forget about it.

Your courtesy is appreciated. I am concerned that the insurer appears to have settled a claim without properly involving your daughter. Can you ask to see any documentation showing that your daughter was in agreement with their action ? if they haven't then I think they have acted incorrectly. I expect the Speed Awareness Course question has been put there to pick up any drivers who would otherwise have had points on the licence and have to pay a higher premium. Anyone taking the course will have been stopped by the police for speeding and be considered a higher risk. The onus now is on insurers to ask the right questions and I think it is a legitimate question.