Yikes, I guess this is a good argument for always printing out a hard copy boarding pass at the airport (and saving it).
Does she remember the name of any of the flight attendants (or even better, the captain from when s/he introduced him/herself)? Perhaps even the UK entry stamp from the passport, would at least prove she arrived in LHR on the scheduled day.
But frankly, I'm not sure how EC261 applies w/r/t being IDB'd. The passenger didn't have a confirmed reservation for that flight (since it was cancelled), and the passenger *knew* she didn't have a confirmed reservation since the phone agent told her so.