I agree with you, even though I've never served.
Say what you will about Steven Spielberg, that opening scene is one of the most amazing things I've ever seen in cinema.
The only rap I have against Saving Private Ryan is that it DID NOT include the seminal quote of the day on Omaha Beach - by Colonel George Taylor.
When all of the men were pinned down and NOT going anywhere, Colonel Taylor strode up and down the beach amidst withering fire from the Germans and said:
"There are two kinds of people who are staying on this beach: those who are dead and those who are going to die. Now let’s get the hell out of here."
And, thats EXACTLY what they did ...
BTW: Robert Mitchum played Colonel Taylor and delivered the quote in The Longest Day ...