Why do you think that Bilbo thought he had a right to the Arkenstone? What makes him think that?
In my book on page 235 Bilbo is basically manipulating the fact that the company said he could choose his own share. Bilbo says"They did say I could pick my own share;and I think Iwould choose this,if they took all the rest!"
He is clearly using what they said and took what was not his.
