When Aeromexico's site suggests economy is "sold out" on all their flights between Mexico and China or Japan, does it really mean "sold out"?

An airline can zero out inventory in any fare they don't want to sell, for example

• If they accidentally posted the wrong fare (e.g. $90 instead of $900), they could zero out a bucket to prevent anyone from buying it.
• If the airline or route are suspended (e.g. diplomatic or regulatory issues), then all seats may be zeroed out, because the route is not canceled and the flights will presumably resume, but you don't want people buying seats on flights that won't operate.
• The same goes, of course, for flights that will be canceled before the end of the schedule.

Airlines do this all the time, and what you refer to as a "crappy tactic" is also the normal way airline seats are priced. A certain inventory of seats is available at certain fares. If demand is lower than projected, then the airline will release more seats in lower fares trying to attract sales. If demand is higher than projected, they won't, and they may be content to sell only full fares if they can fill the plane.

Here, the more prosaic explanation is that demand is indeed outstripping supply. Flights between China and the U.S. are completely sold out in certain months of the year, and there are far fewer seats between China and Mexico as opposed to the U.S. AeroMexico's PVG-TIJ flight operates only three times a week. There will be business travelers to TIJ (or going onward to MEX), but also people flying onward to Central or South America for whom the TIJ flight avoids needing to transit the U.S., while being far more direct than flying via YVR.

Second, the airline may set aside a large number of seats on some flights for sale through consolidators— it may be that the low fares you saw advertised are only available booking through a consolidator. This further constricts the supply of seats available for sale directly to the public.