And, of course, I've had many similar experiences in Japanese, for example with distinctions that don't exist in English ("watasu" versus "tsutaeru" for "convey," depending on whether the object is a thing or a message, for an example that came up very recently), or indeed ones that don't exist in Japanese ("ashi" means both "leg" and "foot," to take one of the more mind-blowing ones).
Today my friend Mami was telling me how someone had stolen her friend's bag when she was travelling. I can't remember what she said, but it was slightly off, grammatically, and I corrected it to "Your friend had her bag stolen."
This confused her, as well it might, since the construction looks exactly like the one we use when we purposely arrange for someone to do something for us, e.g. "I had my kitchen rewired." I'd never noticed the similarity before. Indeed, it only works when referring to the subject's own property: "I had your bag stolen" sounds as if it's spoken by a criminal mastermind.
Are there are any other verbs that allow a similar construction to "I had my bag stolen" (i.e. someone stole my bag)? I can't think of any right now.