Let's start with what an Uchiha is:
Uchiha is a clan that represents a group of people whose power lie in their emotions.
They can achieve their ocular changes through emotions that hold a heavy impact for them. Example: loss, sacrifice, etc.
The base powers of the Uchiha:
1. Read the motion of the person they are focusing on;
2. Genjutsu;
3. Body - Eye perfect coordination;
4. Perfect Visual Memory;
These are the base powers of an Uchiha. These are the powers that make an Uchiha, Uchiha.
As time passed by and the manga progressed Kishi slowly started to fade away from all these fundamental characteristics.
Now, let's cut the chase a little bit and get to cake faster.
The Rinnegan.
The Rinnegan powers:
1. 6 Paths
2. Limbo
3. Share vision
4. See Limbo world
5. Probably more, but I don't remember any more at this point.
There is nothing in the Rinnegan similar to the Sharingan power. No power whatsoever.
There is nothing of the powers that make an Uchiha, Uchiha within the Rinnegan.
Therefor I believe that calling an Uchiha with rinnegan, an Uchiha is a complete hurdle of donkeys because the fighting style is changed at an 180 degree angle.
Many people and I've read this a lot, treat a rinnegan user as a sharingan user. Why would they do this ? Rinnegan has absolutely no power connection with the demon eyes.
These three guys explain it better than me. I actually lacked the skill to express what i wanted to share with this thread and they helped me a lot. If you don't understand my words. Read their words and you will.