@FredKFredK,

You are most likely correct, but it would be recommended to have an electrician take a look to make sure, as the process to confirm this involves leaving exposed wires and connecting circuits to test for hot wires.

It is always safer to have a separate ground connection. If your house is older, I would be more concerned about the presence of a neutral wire. Neutral Wires did not become standard practice until the early 70s. The Neutral Wire is absolutely required and you can't get around not having one.