Michael, you are mixing two different things here. In the previous question we were discussing the effectiveness of using fill light to distinguish areas on the subject. Traditionally, a fill flash is used to bring a subject's brightness level to be less contrasty with the background, such that metering for the subject will not blow out the background, and metering for the surroundings will not underexpose the subject.
So, the answer to the question is yes, fill flash certainly helps bringing out details of a subject over a bright background.
EDIT: reading the comments below, I think I need to clarify the terms I use in this discussion. By referring to dark and bright areas on the subject I mean dark colors (i.e, black) or bright colors (i.e, white). Think Dalmatian. The argument in the previous question was that shedding light on the subject will not reduce the dynamic range of the light reflected from the different areas. Through the comments there one can see that a conclusion is that given multiple lights, then increasing one source's intensity can indeed reduce the DR.
In this question, the OP asks about the effectiveness of fill flash, and here, the problem is not the DR of the subject, but rather the whole scene.