Idsant, sorry to hear of your loss. It sucks, I know. I had my purse stolen in London last year and lost EVERYTHING including my passport (and my favorite purse). Fortunately I was with my partner who was able to vouch for me, etc, but what a sick feeling that is.
I've heard many travel 'experts' say you're supposed to leave your passport in a secure place back at the hotel, but I stay at a lot of hotels I don't feel so secure about. I'd rather have my valuables with me.
On a different trip, my employee kept nagging me to leave him a copy of my passport, etc. I finally did it the morning I was leaving. I was getting into the limo when I realised - my passport was still on the scanner! Oops.