This may be a very rare chance for me to go into more detail than orbitmic! Though his answer is indeed the bottom line.

Price Promise is essentially about comparing some BA operated, BA marketed, BA metal sets of flights, sold by BA 0 but also sold by third parties, typically Online Travel Agents. It's not about BA having the lowest bucket in all the different codeshare permutations. So if BA flew to Oulu on their metal, and TravelWhatsit.com had a stunning undercut on what looked an identical itinerary, then you are able to invoke Price Promise. But if Finnair package flights under different codeshares to BA, that is out of scope.