Board Thread:Theories and Speculation/@comment-35172651-20180401134411/@comment-734582-20180407154636

HeroOfSacrifice wrote: Neji's father said that Neji did have a powerful Byakugan,infact,one of the strongest out of the Hyuga's. So Neji could've seen more chakra going to the eyes. Again, that's an assumption. Obito has enough chakra to maintain Izanagi for 5 minutes, something Danzo couldn't even do. Every time Danzo cast izanagi it caused a HUGE drop in chakra that Karin could easily notice.

So, compared to Obito's naturally massive chakra reserves, would that bit of chakra going to the eyes even be noticeable? I don't think so, since the team checked for Genjutsu as a possible cause of Obito's abilities. If there was a noticeable chakra flow or chakra drop associated with Kamui, then they wouldn't have thought it to be genjutsu (since genjutsu doesn't work that way).

In fact, the fact that they checked for genjutsu in itself suggests they couldn't notice any kind of jutsu going on with Obito.