Proving that she actually flew the flight shouldn't be super hard:
- There's obviously the passport stamp for the right day
- Did she check a bag?
- Did she buy anything at either airport?
- Did she pay for transportation to/from either airport, or parking at PHL?
- Does she have a smartphone with Google location tracking turned on? If so, her
timeline will show her in both airports at appropriate times
Probably worth sending some set of evidence to AA saying "I really did take the flight--you messed up so please fix". If not, probably using one of the EU-based firms that do compensation claims for her is the best bet since going back to London for the small claims case is probably not worth it.