I skimmed thru the article, but I didn't see where the author gave the "real" number of casualties. I did see some examples of poor logic and obvious bias though.
I'm inclined to believe the number given by the government for the number of US deaths: slightly over 500. My prediction was that that number would be 3000 before then end of major combat operations, which the President identified as May 1. So, I see every day that that number is below 3000 as a blessing.