The entry from TIMATIC for French Polynesia reads as follows:
Document Validity:
Passports and other documents accepted for entry must be valid for a minimum of 3 months from the arrival date.
Admission and Transit Restrictions:
Passengers and airline crew who have been in Cambodia, China (People's Rep.), Chinese Taipei, Hong Kong (SAR China), India, Iran, Italy (Emilia-Romagna, Lombardy and Veneto regions), Japan, Korea (Rep.), Macao (SAR China), Malaysia, Nepal, Singapore, Sri Lanka, Thailand, Philippines or Viet Nam in the past 30 days must have a medical certificate, dated from maximum 5 days before their arrival in French Polynesia. The medical certificate must confirm that the passenger is free from Coronavirus (COVID-19).
Visitors must hold return/onward tickets. Information: Passengers leaving French Polynesia by private boat who do not have a return/onward ticket must obtain a guarantee letter from a shipping/fishing company. This does not apply to nationals of EEA Member States , Andorra, Monaco, San Marino, Switzerland and Vatican City.
This appear to mostly mirror the direction issued by the French authorities:
Renforcement des mesures prises par le gouvernement pour éviter l'entrée du coronavirus 2019-nCoV en Polynésie française - DSP , although the requirement for travellers from 'Asia, Japan and New zealand' needing a medical certificate not older than 15 days is missing. Although I wonder if this has been replaced by the more rigorous '5 day' requirements.
Not sure where smartraveller gets its advice that all travellers require the medical certificate... the link the provided (earlier in my post) does not support this, although as per edit below, the UA tool is far more general in its advice.
Understand your frustration re Brazil - but the airline's information on visa extensions is probably outside the remit of TIMATIC. That's there to determine if you are able to board based on your current status at the time of check-in.
Edited to add: interestingly the UA version of TIMATIC states:
French Polynesia - Destination Passport
Important:
All passengers are recommended to present a medical certificate dated from maximum 5 days before their arrival in French Polynesia. The medical certificate must confirm that the passenger is free from Coronavirus (COVID-19).