I spoke this evening with a representative of Freedom Now, the group that has worked for Liu's release after his imprisonment and issued the open letter. Here is the news, from Freedom Now's perspective, on why those three people did not sign.
Barack Obama didn't sign because he wasn't asked. That is because the letter was addressed to him, along with several other heads of state, asking their support for an entreaty to the Chinese government. Even if he had been asked, Obama would not/could not have done it: as a sitting head of state, he can't really sign things in a personal capacity. (The same would apply, despite their less powerful executive roles, to Nobelists Shimon Peres, president of Israel, and Jose Ramos-Horta, president of East Timor.)
On the other hand, in his role as U.S. President Obama did all that the Liu family and Freedom Now could have hoped, in immediately issuing a White House statement congratulating Liu and urging the Chinese government to release him.
Nelson Mandela was hard to reach, for health and logistics reasons. Desmond Tutu himself was (as has been reported) away a prolonged ship voyage for "Semester at Sea" teaching duties and not in a position to make sure Mandela signed on.
Al Gore didn't respond to numerous faxes, phone calls, letters, and messages. The Freedom Now people believe he received their requests, though they can't be sure. In any case they say they never heard back from him.
They didn't even bother asking Henry Kissinger.
The name on the signers' list that most inflames the Chinese government is the Dalai Lama's. Was there any hesitation about including him? The Freedom Now official pointed out that on the morning of the selection, Liu Xia, speaking for her husband, began by thanking three people who had nominated him for the prize: Desmond Tutu, Vaclev Havel, and the Dalai Lama. (PDF of statement here.)
After the jump, a few messages from readers and other links. Then the "mystery of the Nobel letter" is finished here until further notice.