This whole less than illuminating discussion revolves around the meaning of the word, "style," and nobody's really tried to attack that bag of worms. Does the way you "point" a camera constitute a style? Well, if you want that to be your definition, then I guess you can have that as your definition. The guy to your right will have a different definition and the guy to your left will have a different definition, and Jeremy will have another definition that probably will defy analysis.
How is "the way you point a camera" fundamentally different from "how a painter holds her brush"?
The perceived significance is highly subjective - my Aunt would perhaps not have a specific way to handle her camera that would be recognized by Art Photographers as an individual "style". Then again, she might do something that does make her stand-out from the typical photographer (in a neutrally way).
Perhaps the issue is that some like to use "style" to also mean some positive description (i.e. "good", "well thought-out", "art"), while others use the term simply to mean "those aspects of one photographers image that tends to be different from those of another photographer".
I tend to think that for a photographer using e.g. "highly visible HDR/tonemapping" or only snapping "Moose in the sunset", it can make sense to describe this trait of their photography as it separates them from many other photographers. Call it "style" or whatever you want.
-h