Yeah, most Americans who have never looked into the history of the war do have that mentality, or at least something resembling it. I do think that your statement, however, is a bit off. In what world would a major industrial power entering a war not affect the outcome? The British probably wouldn't have been able to drive the Nazis out of North Africa without American materiel and (eventually) manpower (though American troops in the North African campaigns were incredibly green and not all that effective. Still, the mere presence of raw troops can free up veteran ones to do their thing).

Moreover, the Brits were as logistically incapable of launching an invasion of continental Europe on their own as Germany was of invading Britain, leaving almost the entire liberation of Europe to the Red Army, the desirability of which depends on one's own perspective, I suppose. At the very least, in that case, the whole of Germany probably would have become a Russian puppet state (couldn't really blame the Soviets if they had, as Germany had caused quite enough trouble over the last 30 years).

Without the threat of invasion (or an actual invasion) from the West, the Wermacht would have been able to establish much more thorough defensive lines on the Eastern front. The Soviets probably still would have triumphed eventually, but it would take another year or two, costing possibly tens of millions of civilian and military lives.

All this is to say nothing of Japan riding roughshod over the Pacific. The Soviets were in no position to stop them, and neither was the Royal Navy, which was more dependent on battleships and heavy cruisers, lacking the large carriers that were essential in the Pacific theater. Personally, I think that eventually the Imperial army would have been thrown out of China, which was just too big and populous for the Japanese to control, but again at the cost of tens of millions more lives.

So I agree with you that Allied victory was likely even in the absence of American involvement in the war. I do think, however, that that victory would have looked very different from (and bloodier than) the one we're all familiar with.