Literally, in a manga:
- Hagoromo says that Madara received the power of the chakra (Hagoromo), not the chakra itself Hagoromo.
- Several times it is emphasized that the chakra Six Paths can be obtained by becoming a Jinchuriki Ten-tails or can be obtained directly from Hagoromo.
Rinnegan does not give Hagoromo chakra. Just as Sharingan does not give the Hagoromo chakra, although he has been mentioned several times as the power and eyes of Hagoromo inherited by Indra.