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.