On the Documentation pages both for Graphics and Button only the two-argument form of Button is mentioned as a wrapper allowed inside of Graphics. So I would not say that the behavior you describe contradicts the Documentation.
From the other side, for what purpose may you need a knowingly inoperative Button inside of Graphics? This approach looks like a wrong idea on its own, so I would not complain that it produces an error message. Button without the second argument is just a useless wrapper and the error message correctly warns that you are doing something wrong.
You have already provided an easy workaround - simple addition of the second argument of Button (even Null) "fixes" this: Graphics@Button[Disk[], ] does not produce the error message.
So there is nothing that can be called even a minor bug.
Why then your workaround through editing the output by prepending Graphics@ to it works? Let us see what the output Cell actually contains by appending //InputForm and evaluating inside of a Notebook:
You see that the Button in the output Cell actually contains four arguments (but it is still the one-argument form of Button with options appended)! So the explanation is simple: Mathematica simply checks if Button contains only one argument and complains in this case. It seems to be the intended behavior but poorly implemented: more general case of one-argument Button with options was not considered by the developer. So it is not a bug, just careless without harmful consequences.