I guess we can say the Routing Table is the World Championships and in that best athletes (routes) from different countries (routing protocols ) participate .
So to identify the best athlete in a country is the responsibility of that country
So here BGP selects the best route to reach to x.x.x.x route and iBGP and eBGP give the best route and BGP says that for us eBGP is the better route and i am not checking the AD value its because of best path selection criteria
But then in the Routing Table (World championships) x.x.x.x route is given by lots of countries like BGP,RIP,OSPF,ISIS and EIGRP and now AD value comes into picture
So inside a country we trust all citizens so not checking AD value inside a country but in world championship we have to trust a country based on their trustworthiness using AD value
I hope this is the right analogy for my understanding