I feel like you were reading a different sentence than what i wrote. Fortunately, that was "COAT is not real" which is basically the same thing.
Anyway, COAT has only ever been described once by Obito. The only source of information Obito could have had regarding Hagoromo's abilities at that point was the Uchiha Tablet, which is not a reliable source. It skipped Hamura, and was all part of BZ's evil plan, and is therefore not reliable.
Any times people have claimed COAT has been used, it's actually just either extremely high speed regeneration or Chakra being sentient on it's own. (People forget that a lot)