Because they are there to control the CEO if he is too bad for share holders' value. But they didn't do it in the Solar City buy out, because this is not an independent board, I think at least 2 of them are relatives.
Now this time it is different (from the SC example) because Musk's claim is just outrageous. First he has no new ideas to profit from, second what he demands is unheard of. So if the board let him get away with it by issuing more shares, the share holders could sue the board because they didn't act in their best interest. (actually there was a lawsuit based on the SC bailout too, but they came up with some bullshit excuse) That lawsuit was eventually dismissed.
I would imagine this would result in a huge class action from shareholders.