The use of the term "New American" dates back to the early 1980s, a time when there was a great deal of new interest in American food. The first use I've found of the phrase "New American cuisine," as opposed to "the new American cuisine," was in the transcript of the first Symposium on American Cuisine, held in Louisville, Kentucky in March 1982. For several years preceding that conference there had been a rebirth (and in some cases birth) of regional American cuisines, sometimes based on traditional dishes of a region, and in every case oriented toward the freshest, finest ingredients a region had to offer.
At the Symposium, and those that followed, there was a lot of very self-conscious discussion among chefs, journalists, critics--and pre-chowhounds, if you will--about what New American cuisine should be. One camp thought it should reach back to traditional American dishes that were forgotton or endangered, and the other felt that New American cuisine would benefit by embracing foreign influences. At the same time, a number of chefs (Mark Miller, Robert Del Grande, Bradley Ogden, Paul Prudhomme, Marcel Desaulniers, Jimmy Schmidt, etc.) had begun to construct completely new cuisines based on the best ingredients of their regions.
The two things all the factions agreed on was that the primacy of ingredients was all-important, and that technique should be French.
While no actual consensus was ever reached on the regional American-vs.-foreign influence issue, things have gone pretty much in the direction of embracing foreign influences--particularly Asian and Latin American, along with Med-rim.
I think the reason people are confused about what New American cuisine is is that it has never really been clear, especially when you think that traditional American cuisine was based largely upon French and English, and we built a new cuisine using French technique, American ingredients, American ideas, and foreign influences.
Longwinded as that was, that's a short answer to a complicated question! Hope it helps...