Let me ask you all this. Do you remember some event EXACTLY how it happened 10+ years ago? Sure, something like that SHOULD be forefront in your mind and 100% unforgettable but when you consider how many OTHER tragic or memorable things that man has done, seen or reported on since then it could be VERY easy to jumble up events. The dude found out about, kept quiet about and then reported about one of his best friends and colleagues being TAKEN HOSTAGE by enemy combatants. I would certainly think THAT could cause a string of events that happened years prior to be jumbled a bit in his mind.
Let's be honest here, it's not like Williams was trying to come off sounding like a hero himself. He was acknowledging heroic acts toward him by a soldier, which may not have been AS heroic as he made them out to be initially, but should still be considered heroic just for the fact he is serving our country in places or situations many of us hope we never see.
Maybe I try too hard to see the good in people, but I really think it was a matter of misremembering the exact order of events. Yes, he SHOULD have done some due diligence to check with someone to make sure the facts were right, but maybe he wanted to surprise the soldier with his acknowledgement of his actions.
For his lack of due diligence on confirming he had the story right, he deserves some time off, but I don't think he deserves to lose his job over something that could happen to ANYONE (misremembering the order of events, not the actual event that happened to him).