I've heard everyone say the longer the focal length, the smaller the dof, but does this statement take focal distance into account?

I can totally understand it if the focal distance is the same, since with a wide angle lens, anything more than a kilometer away is basically on the same plane to the lens(sense of depth gets lost at far away), so focusing on anything in the background gets the entire background in focus.

If we use a long focal length, however, even if the subject is quite far away, it looks like it got pulled closer to the camera, and the background is too far away to be in focus(taking a portrait of the subject from far away).

Let's say we shoot at the same subject with a wide and a long focal length at the same f stop, but we shoot the long focal length shot further away from the subject, so that the subject in both shots is of the same size.

In this case, does the long focal length shot have a shallower dof? In my understanding, the background is only enlarged due to compression, rather than being less in focus.