The text on the Gleim website appears to be correct for the FAA situation, so feel free to use that. Going back to your original question, yes, under FAA rules any training received should be logged as dual. If you are continuing for your CPL, ME and/or other ratings it is useful to keep track of the various requirements needed for said ratings, the needed cross country hours for example. So make sure to log all this stuff correctly. The best place to discuss this is actually your instructor, he/she should be able to explain the details.