Can Timatic data on some sources be outdated or incorrect?

Oh yes, for sure! In my spare time I liaise with the IATA sourcing manager on an unofficial, voluntary basis, and can't count the amount of corrections I've had to request over the years (after verifying facts with national authorities). A correction hasn't always turned out to be justified (with authorities occasionally giving me erroneous info), but a significant amount were.

It's usually IATA's national sources that are at fault, such as sloppy/imprecise communication, laziness about reporting changes or failure to mention one or more existing exemptions.

Once in 2017, I can only assume IATA's sources in Italy had been smoking something (no joke!), and I was denied boarding on a flight to Italy due to it (but managed to get re-booked for free and receive €400 compensation). I immediately alerted my IATA contact and TIMATIC was corrected pretty soon.

So yes, TIMATIC is usually the most reliable source there is (other than emailing the actual authorities) but very much not 100% correct about everything.

As for the specific case: you could try messaging timediting@iata.org and sourcing@iata.org attaching the link and pointing out the specific exemptions. With their vast amount of workload, though, I wouldn't hold my breath for them to acknowledge it (even I haven't really been getting through to my contact lately)

The Timtac entry is correct and covers the exact situation you are describing.

The entry contains the text :

This does not apply to residents of Japan with the Letter of Confirmation of Submitting Necessary Documentation for Re-entry into Japan, and a medical certificate with a negative Coronavirus (COVID-19) test result. The test must have been taken at most 72 hours before departure and the sample collection method must be 'nasopharyngeal swab' or 'saliva'.

The relevant phrase here is "Letter of Confirmation of Submitting Necessary Documentation for Re-entry into Japan". This is a document issued by a Japanese consulate which allows a passenger meeting specific requirements to enter the country. (Note that whilst it states "re-entry", there are multiple reference to it also being used for initial entry).

The document you have link to is not a definitive list of conditions as to who may be allowed entry, and in fact specifically states that it contains "specific examples of cases where re-entry or new entry may be permitted depending on individual situation".

The word "may" here is critical here as it implies that additional verification/vetting is required based on the conditions. The Letter referenced above is the proof of that verification, and show that the Japanese government has confirmed that the passenger meets their requirements and is allowed enter the country.

Even outside of this specific example, the simple fact is that Timatic will never be able to cover every single situation. There will always be corner cases where Timatic will state a passenger can not travel, but if the passenger is able to provide suitable documentation to confirm their will be admitted into the foreign country (normally in the form of an approval letter from the relevant government) then they will be allowed board. Situations like this will normally result in delays at check-in so it's always a good idea to arrive early to allow any additional checks the airline wishes to do to be completed.