He told her to expect a letter with the cost of the ticket and a fine. That if she wishes to appeal, it would go to court.
Then it's reasonable to hope for an out-of-court settlement (or possibly not even that, if it turns out she hasn't done anything "wrong"). Only a court can issue a fine.
It might not be completely surprising if a staff member said things which are more acceptable to the passenger than what transpires later. Hopefully an inspector would be more likely to say things that are accurate.
In the meantime sit down with her and make some notes
Could it be useful if she writes down, today, what she remembers the inspector saying and what she said to him?
She could note where she is sure of the exact words - while being aware that people can think they've remembered things accurately when they haven't.
If the inspector said the company would offer a settlement but the company doesn't immediately offer one, maybe a note of the conversation would be useful. She might as well write it down now, partly so that she can if necessary say "I wrote this the next day". I'm not saying the company would definitely stick to what the inspector said, but perhaps a court might regard it as abuse of process or look more kindly on her if she was convincing that she had been misled. So the prospect of either of those might be one factor discouraging the company from taking it to court.
If he misled her about the legal position ("Can't leave"?) or otherwise behaved unsuitably, that might form the basis of a separate complaint, or possibly useful background for responding to an allegation of an offence - but lack of solid evidence might be a problem.
Writing things down now could help avoid confusion later, even if they won't make a big difference to the action she takes.
can’t be clear whether she’s likely to be prosecuted or just fined.
It depends on:
a) what's happened;
b) what the company/their agent thinks of it at various stages; and maybe on
c) what she does at various stages.
The company could abandon talk of prosecution at any point. So if necessary your daughter could keep trying to persuade them to settle. It's even possible to turn up early at the court, ask staff where the prosecutor is, and attempt to persuade them in person. Even if she's broken the law, if she shows signs that she's learned from the experience and won't do it again, those would usually be factors in her favour.
If the company makes noises about moving to prosecution, some people would hire a lawyer - and that could have more effect. As you can see from this forum, after advice from here, often people don't need a solicitor.