What if, as in this case, they both wrote it?

Per the spirit of the "rule" (whether it reflects reality is a different question), I'd say that what matters is whether or not the first CEO took part in the announcement at all. The fact that the new CEO also wrote something seems less significant.

Apart from a few special cases, it is always the board's choice.

If you have experience/more info around this area I'd love to hear. Never having attended a board meeting, I'm reliant upon others' pithy quotes.

It is the board's job to appoint the CEO. There are subcommittees formed to do this, which the existing CEO usually stays away from, because in almost all cases there is a reason the CEO is stepping away/being made to step away in the first place.

Heck even in Steve Jobs' retirement letter (https://www.apple.com/newsroom/2011/08/24Letter-from-Steve-J...) he didn't appoint Tim Cook CEO but rather "strongly recommended" him to the board.

Ah I see what you mean. I think the quote is referencing the choice to step down, not the choice of successor.

absolutely false.

founding CEOs have different powers than appointed ones.

Nope. It is true. The board has the power to hire and fire the CEO. Sometimes a founding CEO has sympathetic friends on the board and can arrange the company to be able to nominate board members.

BUT, board members are not answerable to the CEO. The CEO answers to the board. That is one of the reasons for a board of directors...

Only if they have control of the company and the board seats to go with it.