Madara eyes are not "Sharingan" anymore because it's a Rinnegan, the scan just shows Madara hyping himself nothing proves that he lost his Sharingan abilities. If we talk about Mutations then Kaguya's Rinne Sharingan was said to have Sharingan abilities so the Rinnegan, the mutation of the Rinne Sharingan lost those abilities yet the Mutation of Hagoromo's Rinnegan the Sharingan had those abilities. Mutations have nothing to do with this, Hagoromo never awaken the Sharingan's Dojutsu (Susanoo, Tsukiyomi) so his Rinnegan only has the Rinnegan dojutsu while Madara eye's had previously awaken both MS and EMS so his Rinnegan is the evolution of his own "eyes". Though I believe the Eye's abilities/ techniques are connected to one's brain that's why Madara could use Susanoo blind.
Bold: Not important and confusing, take away the bold and it still makes sense.
TL;DR
If Nagato awaken the Sharingan dojutsu previously he should be about to use Sharingan techs with the Rinnegan via his brain but he didn't and his not a Uchiha. He had the final product (the Rinnegan) transplanted to him so he only has Rinnegan techs. Make sense?