This happens to me. I have a common real name so my gmail is used by all sorts of people. I am married and get signed up to dating sites that don't verify email. It is embarrassing.
I've been in the unfortunate position of receiving very confidential financial documents, which I could have done a lot of damage with.
Most times I have sent a friendly "this is not the person you think it is" type reply, but with automated systems, this is impossible.