I'm currently a junior in an American Integrated Studies course at my public high school. Our teachers (we have two since it's both an american history and an english class together) have a blog, http://www.anamericanstudies.com/ that they have us students post on on a weekly basis. Since you mentioned (well, heavily implied) that you had issues with how public schools taught American History, I figured you might enjoy checking out the blog. (Due to scheduling conflicts, I have regretfully had to drop that American Integrated Studies class and was assigned into another one)
Basically, my line of thinking is that all three conflicts were caused by the existence of geographic empires, and that all three conflicts were about said geographic empires and who was allowed to have them. It began with anti-Imperial nationalist movements in 1914, and ended with the break-up of the Soviet Bloc between 1989 and 1991. (Those who recently started following me can find a much more in-depth discussion of this here).
The argument that WWI and WWII were the same war follows that same general line of thinking. However, I think that the connections between WWI and WWII were much more tenuous than many make them out to be (you can read more about that here). World War I caused most of Europe to fall into economic ruin. That economic ruin caused people to lose faith in democratic forms of government, and look to fascism instead. The aggressively imperialistic behavior of those fascist governments—specifically of Germany—is what caused the Second World War to begin, and empire is what allowed it to grow and spread from the Atlantic to the Pacific.
So, in discussing WWI and WWII, the connection exists, but, in my view (others may disagree) it is fairly weak; it is only in the larger 1914-1991 context that it becomes clear that they were all stages of the same general conflict, and representative of the breakdown of the same general mindset.
I hope that was clear/answered your question adequately. If not, let me know and I’ll try to expand on specific points for you.
Thanks for the link; I will definitely check that out. (Amusingly, I received this question just as I was starting a post about my issues with how public schools teach American History).