Well if Timatic says "Visa required, except for Nationals of <visa exempt nation> holding
confirmed onward airline tickets to a third country, if arriving in and departing from the same city" isn't the concern here with Timatic, not AA.

Seems to me that the OP did not hold onward airline tickets to a third country ... he apparently had a flight to a third country with a connection back to the US, but the ticket is to the US, not to a third country.

Obviously, the appropriate governmental agency in China could create a 144 hour tourist visa but they didn't. Instead, they created one for someone who was going to spend a couple of days in Shanghai and then head to another country for some period of time. On top of that, they used the word "transit" which has a common understanding in the aviation world. If it was so simple, wouldn't Timatic have caught this? And, if this is a known issue, then isn't someone choosing to connect back through NRT because approach often works vs seeking a 10 year visa for $140 just making their own risk assessment? Lets be real, there are people who will be flagged by Chinese immigration and subjected to additional scrutiny.

So perhaps OP's story to AA should be ---

I saw there was a possible exception to the Chinese visa requirement and for whatever reason, I didn't want to get a Chinese visa, so I contacted a low level person at the Chinese consulate who told me my itinerary was OK. I obviously knew there might be an issue because I printed out this email. The folks at the AA counter took a strict interpretation of the Timatic rules which say I needed a ticketed flight to a third country. We disagreed whether my ticket back to the US that connected through Narita was an airline ticket to Japan as opposed to an airline ticket to the US with a connection in Japan. It took them two hours to figure this out so I missed the flight and had to book at hotel by the airport overnight and pay an extra day parking. They might have thought that I recognized this could be an issue since I brought them an email from the Chinese consulate. I don't really understand why they didn't accept my views that a lot of people on Flyertalk find Chinese immigration officials don't really care about this issue so long as there is a flight out of China that goes somewhere other than the US. I don't really think someone at the check in desk should really worry about getting in trouble since this has worked for a lot of people posting about it.

If you don't want to take the risk, get a visa, right? Then no problems with AA, UA, DL or any other airline using Timatic and interpreting the language in Timatic strictly and applying the ordinary meaning of the word "transit."