[EVERYTHING] Is Tyrion really....

This is my first post here so forgive me if I do/say anything wrong.

I think we're all familiar with the "Tyrion has Targaryen blood" theory (I'm not a fan of this theory). These past couple episodes have been dropping hints of Jon's Targ blood ("I'm not a Stark" Drogon flies by, Gilly reading the text about Rhaegar's annulment and secret ceremony etc etc.). In yesterday's episode we see Jon touching Drogon and noticing something obvious here and we remember Tyrion in the same situation touching Danny's other two dragons. I think we're supposed to assume Dragons don't normally let anyone touch them without ripping/burning their arms off unless they have the blood of men from old Valyria. I noticed the scene with Tyrion and Jamie talking, the camera would have two different shots of each of them every time they spoke and with Tyrion, every shot had a dragon skull behind him. Now I'm not a fan of this theory mainly because I don't like the idea that characters or more important if they have Targ blood in this show and I much prefer that Tyrion is a full blooded Lannister, but a special kind and his father truly disliking him because of his dwarfism. Makes things more tragic, but could those shots mean anything or am I over analyzing?