You are looking at it with the mindset of someone who wants to apply grey emotions and sympathy to a Yes/No issue.
But it's not a yes/no issue. Public perceptions and considerations regarding the damage to the reputation of the parking service are also relevant. People start off disliking them ... so they're usually happy to forego a few pounds if it means avoiding throwing fuel on the fire. Especially when it's pretty easy to demonstrate that the parker isn't trying to scam them.
But her car was occupying a space that it was no longer entitled to occupy. It (she) had broken the contract that she had agreed to by parking there.
Legal contracts can be impacted by the circumstances involved. Is someone required to pay if their car is run off the road and is occupying a space (or part of one) as a result? Or if they parked somewhere, but couldn't leave because a delivery truck double-parked next to them while unloading, and blocked them in?
Neither the parking service or the parker are at fault. They've both tried their best to do what is expected of them. The parker failed, due to circumstances reasonably beyond their control. The result is very much a grey area, but it's not untoward to ask the business to take what amounts to a very small hit, well within their expected loss margins, versus the parker getting a considerable dent in their wallet.
Either way, it's worth appealing. Not guaranteed to work, but it has a good shot. And if it fails, they shouldn't be punishing the parker with a higher fine in those circumstances.