I think the video is worth bringing up. I probably should have mentioned that the ID reports were never even confirmed. I was aware of that but I didn't know that Ryan was the original source of this information so that's interesting to hear.
I did look through the documents again before I first posted and the only information I could locate which pertained to Ryan being identified as the shooter were Ryan's detainment reports, which all confirmed that New Jersey officers had information that he had been identified as the alleged shooter and was presumed to be deceased at the school. It seemed that this mistake was only clarified once Ryan appeared at his apartment in front of the New Jersey officers.
The other document which pertains to the identification of the shooter by Connecticut police and the FBI says this:
[You must be registered and logged in to see this image.]So, the Connecticut police had no real ID on the shooter until sometime around 2:00PM (and Ryan was first detained as a suspect shortly after this) but all of the information transmitted to New Jersey which suggested that Ryan was identified as the shooter was from much earlier in the day because they were watching his apartment by noon.
Assuming that there was no ID, they probably would have first found Nancy Lanza's name from the registration on the car but based on the preliminary descriptions of the deceased shooter, they would have known that it was someone other than Nancy who attacked the school. After this, they must have found information about Nancy's relatives and assumed that the shooter was one of the sons, either Adam or Ryan, because he was using a car that was registered under her name.
They didn't actually decide that it was Adam until much later but for some reason, New Jersey police had been told that Ryan was identified as the shooter. I guess that this is what they meant when they said that the names were transposed but in reality, it seems that instead of transmitting information about Ryan as a possible suspect or accomplice, the information that was transmitted stated that he had been positively identified as the shooter. All of this could have happened without Adam carrying any ID on his body or in his car because they would have been able to access the driver's license information for both of them directly from the database.
In terms of the factual content of the video, I'd say that it's all accurate. There really is no proof that Adam was carrying Ryan's ID and that information doesn't seem to have been recorded by the police. In terms of the commentary, I'd say that he's placing excessive blame on the media. There was a lot of false reporting going on but this was not based on unsubstantiated witness accounts. It seems that the police were the ones with the wrong information. Both of the initial false reports, about the identification of the shooter and about the deceased person at a New Jersey address were documented as being transmitted through police channels, so it seems likely that the media was only reporting what they were being told from official sources. My guess about the false report of Peter being dead at the New Jersey address may be a complication of the misidentification. They found Mrs. Lanza's body at about 1:45PM so if there was information transmitted to New Jersey saying that one of the parents was deceased at the home of the shooter, then they may have assumed that this was referring to Ryan, "the shooter," and his New Jersey address.
I also don't think that the media was lying or misleading anyone by repeating that Adam was probably carrying Ryan's ID. If Ryan reported that, then they had a credible source for the information. It may not be true (and I agree with what the video creator says, that it's very unlikely, because I can't remember reading anywhere that his ID was found on Adam's body either) but it made enough sense to think that it could be true. The video creator also pointed out that the article gives the explanation from the police in addition to Ryan's explanation.
The last thing I'd say is that regardless of the truth or the source of the ID claim, if Ryan believed it, then a variation of the original question would still be relevant. Why would Ryan believe that Adam could have his ID if they lived in different states and had not seen each other in two years? Andrew Solomon repeated this information and he interviewed Peter Lanza long after 12/14/12 so it seems to me that either the authorities did find an ID or that although they never clarified for the Lanza family how they identified Adam (or misidentified Ryan) as being the shooter, Peter and Ryan never questioned the possibility that Ryan's ID could have been found on his body.