Misophist...Not everyones forefathers were pilgrims. Perhaps that is who is responsible for the beginnings of the USA, but in my case, my forefathers were not Americans and did not set foot on these shores until my Grandparents (Fathers side) and Great Grandparents (Mothers side) time.
Do you really think it matters when one celebrates the holiday? Does not the intent in ones heart matter more than the actual date? I think the key word in your last sentence is "probably"...the idea being that we cannot know for certain.
Lastly, the USA of today is not the same as the USA of pre-revolutionary (Pilgrim) days. We are a different people, and not all of that is for the worse. :D