From several posts on the JP Yahoo! Answers it seems the Chuurenpoutou myth was popularized by the 1969-1972 mahjong novel 麻雀放浪記.
Coincidentally enough the manga adaptation of the novel is being scanlated and the first reference to the Chuurenpoutou myth was scanlated just yesterday (ch. 37):
https://mangadex.org/title/5343/tetsuya-jansei-to-yobareta-otoko
The general idea behind the myth is due to the rarity of the 'pure' form of the yakuman, similar to the 13-way wait of the 'pure' Kokushi Musou.
The pure form of Chuurenpoutou is: 1112345678999m
With the given shape, a player can win on any manzu tile 123456789m (the 9 possible winning tiles is the origin of the yaku's name).
However, due to the furiten rule of Riichi mahjong (forbids winning off other players if you discarded one of your own winning tiles at any point), to legitimately achieve the 'pure' form a player needs to complete the hand without ever drawing any duplicates. The occurance of that is rare enough that apparently the hand has been joked about as requiring "a lifetime's luck".