Saving private ryan wasn't the first movie to "glorify" the d-day invasion. There were others before it, like "The Longest Day", a real John Wayne movie.
In that movie, it was depicted that the german officers didn't dare to move their panzer divisions to intercept the allied forces without permission from hitler, who had taken a sleeping pill and could not be disturbed.
If he had been awake and the panzers had moved, who's to say the allies could have landed successfully?
What is clear from the records and the no of medals awarded is the bravery of the american paratroopers, who often had to fight overwhelming odds to secure key objectives needed for the main assault force.
Men like these are what made the difference.