First of all, I agree with your post and this isn't a rebuttal, just a response to the above referenced statement.
Anyway, a lot of the troops that came off Omaha did absolutely nothing but cower until the movers and shakers had cleared enough Germans so that troops could advance off the beach itself.
Now, some part of the troops involved in any battle don't do anything but try to stay alive until its over, but I think that was especially true of troops in their first combat.
Just my .02 on green invasion troops still being green.