I was at Heathrow maybe 90 days ago and British Airways had a brand new 787 (Painted in fancy "Dreamliner" dress and BA logo) parked at a gate as if it was in use. Might be that they were still demoing it/showing it off deliberately but I had the impression it was an active aircraft.
http://www.britishairways.com/travel/bafleet/public/en_gb
Given how LOT only received their first order halfway through November, which was widely announced as being Europe's first 787 delivery (http://www.flightglobal.com/news/articles/picture-lot-takes-...), I think your skepticism is misplaced.
If anything it was probably a meet and greet where the executives (and staff) can walk around the cabin to get a feel for it. They run their entire operation out of T5 now so getting a an unused gate for a 787 wouldn't be impossible. Other airlines are still jockeying for gate space at T1-T4.
A training/demo aircraft makes sense. Not to mention free advertising people like me, sitting in a window seat, seeing that beautiful new aircraft with "DREAMLINER" painted across her body.
Granted, BA is the only Airline besides Virgin Atlantic/America where I have felt like I was treated like a human being... so convincing me to fly on them isn't that difficult.