Careless Driving - But where is the proof?

Good afternoon all - based in England.

My wife has been told that there is sufficient evidence to take proceedings against her for careless driving, but something doesn't seem right.

On 02nd October she received a letter from Thames Valley Police asking if she was the driver of her car @ 16:33 hours on 30th Sept (so two days earlier) saying that somebody had witnessed her driving carelessly on X road. It was her, and I asked if anything strange happened and she said she was driving on the road (40mph limit) and noticed a kid on a bike without a helmet, on a side road, the kid gave no indication of moving onto the 40mph road but suddenly tottered onto it. My wife saw it was safe and manoeuvered around the child, momentarily on the other side, before rejoining her side of the road. It's an A road and there are NO unbroken lines anywhere.

What I find odd is that there are no cameras there at all, but less than 2 days after the event TVP have located my wife (the car is a lease, so correspondence should have gone to the business holding the lease) written to her and got it delivered, which is a miracle in itself. Even when there are official fixed cameras, that process is a lot longer.

After sending back her details we have now received a notice from TVP that there is sufficient evidence to take proceedings against her for Careless Driving, but they are willing to offer a course, rather than go to court.

Whilst I accept there may be some artistic licence on my wifes part (I say that knowing I would probably do the same), I feel like this is a little unfair. If it did happen as she suggests, it would appear she was driving within the speed limit, noticed the danger and took safe action to avoid an accident.

Can we ask for evidence or are our only options to accept the driving course or go to court?

Thanks in advance.