Board Thread:Naruto Discussions/@comment-32624156-20170721153715/@comment-25122992-20170728170847

Nope, Hagoromo clearly meant not just a sheer authority, for a simple reason there was no authority he could've granted to Naruto/Sasuke, but he bestowed them with actual power. Combine it with the fact that Hagoromo admitted trying to fix the mistake by giving his power to both of son's reincarnation, and it leads to the logical conclusion that Asura also received some power of his as his successor.

Just admit it, Hagoromo literally said he granted his "power" not some "authority". And Naruto/Sasuke are the main examples of what kind of power he could bestow, while Hagoromo specially empathised the fact he decided to grant it to both of them, unlike the case with his sons.