Overread: - Thank you for the description that -finally- got it right in my head. Although I sort of figured it was as you described, it's easy to assume that putting an EF 17-55 on a crop body would be the same as putting a 1.6 extender (eg, multiplier) lens on it with a ff body. In truth, it's the ANGLE OF VIEW that gets reduced to that of a higher focal length lens when on a crop body, not an increased focal length.
It's like concentric circles. Consider a lens that projects a 12" diameter circular image. It needs a rectangular "sensor" that is 11.99" diagonally measured (ef, full frame) to 'see' the full picture. Put the same lens on a crop body, with a 7.99" diagonally measured sensor, what the camera 'sees' is only a portion of the full image projected by the lens. By comparison, an EF-S lens projects an 8" diameter circular image. The 7.99" crop body sensor would get the full picture as projected. Putting the EF-S lens on a full-frame body (if possible), there would only be an 8" picture in a 12" area, thus a black area around the projected picture.
I've only had a DSLR since last May. With all the discussion here and elsewhere of 1.6 crop multiplier, it's easy to think it was like having an tele-extender built in, which it is not. Us old geezers will "get it" eventually...maybe tomorrow, next week, next year...
I think I understand it now...