My understanding from the reviews I've read is that it's a standalone story, and doesn't connect with the previous entries in the series aside from sharing a similar historical time period.

It's Standalone, yes.
Has nothing to do with the previous(good) COJ games.

@zeforgotten: Meaning that Gunslinger is not a good game?

Meaning that Gunslinger is an awesome game like the previous good titles.
That meaning that Call of Juarez: The Cartel was a whole load of shit, piled on top of a big pile of dead puppies soaked in shit.

You forget the face of your father.