A relative of mine had her passport stolen in Rome the night before her scheduled return (FCO-ZRH-DFW). She immediately called the Embassy, and was not able to travel until they provided her with a temporary one, which took a day or two. I called AA back in the US for her (Exec Plat desk at the time), and they were quite accomodating--it was low season, but they were willing to allow a "few days later" standby, and to spend time checking through the SWISS flights to see what was open, etc.
Interesting about the BA/letter story--she'd never have thought to try that, and the embassy folks didn't bring it up.
IIRC, her passport was actually turned into a police station in Rome a few days later, but at that point it didn't matter.
-Hayden