I've been thinking about this "essentials" vs. "statements" issue the past few days. To me, a big part of the confusion comes down to how we choose to interpret those two labels. Once you move away from Angie's definitions, the usefulness of her system isn't as apparent. .
If you think of an outfit in the same way an artist thinks of the composition of a painting, it seems that Angie is using "essentials" and "statements" in the same way that an artist uses positive and negative space to create balance and harmony in a painting. I'm definitely a newbie in my artistic attempts, but I quickly learned my beginner's tendency to fill a picture plane with subject matter led to a chaotic mess. As soon as I grasped that negative space (the area around my subject matter) was just as important, my compositions became much more interesting and pleasing. Negative space acted as a support system; it didn't take attention away from the positive matter, but complemented it. To me, that's what Angie seems to be alluding to with her "essentials" and "statements".
Negative space doesn't have to be a neutral colour, although it can be, nor does it have to be a solid shade. Even a brief tour through an art gallery will give you a sense of how creative artists can be with their "backgrounds". Sometimes the negative space, in the hands of a talented artist, may even subtly dominate the composition--but the negative space still exists to support the subject by providing a place where the eye can rest.
I think of my "essentials" as negative space for the focal point of my outfit. I choose my statement piece and then choose other pieces to act as my support because I want an outfit which is dynamic but harmonious, and not just a confusing jumble of objects. If I choose to introduce secondary focal points, I need to remind myself they are there to reflect and support, not to compete, with what I've chosen to highlight as my main statement The big lesson, though, is to not make the newbie error of dismissing the importance of and inherent creativity in creating a good support structure, or negative space, for my main player.