I've seen something like this. It could be a situation where they were transitioning from that backup service to their own server or another service, and the move was never completed due to some hiccup or priority change.
But if no one is watching to ensure the move was finished (or they got distracted), then something many people treat as set-it-and-forget-it could easily get into that state.
I don't think it is that far-fetched. I've had experience with a well known company that does millions in revenue per week (web based shopping cart) that just FTP's everything with no DVCS. Designers, developers, managers all have access to the server and db.