In simple terms, she wasn't actually been fined by the police, she was issued with a fixed penalty notice.... she has the option of either paying the fine or challenging it in court - the decision is her's and it's all explained on the FPN.
If she's now paid it then that will be the matter over with - she can't appeal now unfortunately.
Police Officers do not have to witness everything in order to arrest/summons/issue an FPN (how many crimes would be solved if they had to be witnessed by a police officer prior to arrest?) Very often they have to act on what they are told and investigate it from there.
Unfortunately, for as long as police officers' performance is judged on crimes solved rather than crimes prevented, minor crime like this will continue to be dealt with in this way. It's one thing for the government to say they want no crime.... but while minor punishments are given out, and police are judged on solving rather than preventing crime it won't change. Why do you think so many Police Officers are leaving??