Think of it this way: Jeff Bezos is a majority shareholder (at least according to reports, he is not taking on the chairman/CEO role). Normally, the only control a majority shareholder has is to elect/remove the board.

If he attempts to effect other control, particularly by suggestion to the board/whatever, they need to make disinterested decisions.

So the short answer to your question is "always". Every board decision needs to be made by disinterested directors after full disclosure of the facts by any interested directors. Anything else would be a self-dealing transaction, and would possibly subject them to personal liability.