Also possible that Kyle was decorated for highly classified missions and those awards may not show up in Navy biographies and personnel records that can be released to the public.
During Vietnam, scores of USAF pilots flew for Air America, the CIA’s aerial support operation. Officially, they “resigned” their commissions before joining Air America, but they actually remained on active duty. Their personnel records were moved to a secure area within the USAF Personnel Center. As far as I know, their performance evals and decorations earned while flying with Air America never entered into their “official” records, because so much of what they did was classified.
I will defer to those with more expertise in these areas.
Awards for clandestine missions would make sense. If a mission were secret, the award citation would be classified.
I think you are correct. He is claiming those he was awarded, not just those he was awarded publicly.