You are absolutely correct. Focal length is focal length, regardless of the lens design.
While the spacing between the lens mount and the film (sensor) plane is identical for the two lenses, The EF-S lenses have two significant differences in their design, when compared to EF lenses. The first is the size of the projected image. The EF lens design must cover a 35mm film frame while the EF-S lens needs to cover only the APS-C sensor area (a significantly smaller area). The second difference is how far the lens can physically project into the mirror box. Many EF-S lenses would crash into the mirror of cameras they are not designed to fit (at some focal length settings - most EF-S lenses are zooms).
While an EF-S lens covers less "film" space, the size of the items within in the image they do project are identical to that projected by an EF lens of the same focal length. This assumes that you take two photos from the same spot with EF and EF-S lenses mounted to the same body and set to the same focal length.
Additionally, nothing about ANY lens changes based on what camera body format you attach it to. An EF lens does NOT change when you put it on a 20D instead of a 35mm film body, for example.
Further, there is no such thing as a "multiplier" when you put a lens on an APS-C camera. The only thing that occurs is that less of the image will be recorded as compared to using the same lens on a 35mm film camera. It is the field of view that changes when you put different bodies behind a lens, not the focal length, and the change in field of view is totally a function of the body format (size of the film frame or digital sensor).