I am just proceeding with caution. Right now they are not independent. I do not want people approaching them with out some sense of caution. Right now to everyone is a friend, yet we both know all people who won't be. People can be mean.
Dragons have been gone from Westeros for over one hundred years. So they are quite the sight. They know the rules, but I don't expect all people will follow the rules. One should respect them. Any animal tame or not lives on instinct.
To really answer your question, that is the way it is. Many animals are tame, but still wild at heart. Knowledge is power. I am not familiar with animals here except for Jon's direwolf, Ghost. He is tame, but still a wild animal if that makes any sense.