Depo-Provera - could my mother accidently taking depo provera at the doctors office while she was?

Officially you'll be told they don't know. Personally, I'd say absolutely, yes. There are warnings that a person should be tested for pregnancy before being given the Shot. It is not good for the unborn child. I think you'll struggle to get concrete proof of it, but I don't doubt it for a moment.
Look at the ingredients of the Shot, then do some research on what each one can do to your own body, let alone that of an unborn baby.
PM me if you want to know more. My answer will only get removed if I type more. In fact bit may get removed, anyway!
I'll add you as a friend, & if you want to add me too, it'll let us PM. I can give you some pointers. Will prob be tomorrow now, though.