Is there more to this 'mistake' than meets the eye? Further researching on the web reveals the possibility that Taiwan may have been or is still interested in at least the knowledge of how to manufacture nuclear weapons.
http://www.globalsecurity.org/wmd/world/taiwan/nuke.htm
The above article dismisses the thought that Taiwan has the capability to develop nuclear weapons but makes strong claims about their desire to understand how nuclear technologies work. This knowledge could help them develop weapons in the future if the need were to arrive. So, why would the U.S. want to provide Taiwan with nuclear knowledge? The next article gives many reasons why the U.S. would like Taiwan to maintain peaceful relations with China. They are the very same reasons why the U.S. needs Taiwan to work through the U.S. to maintain peaceful relations. While reading this remember the saying "keep your friends close and your enemies closer".
http://www.yomiuri.co.jp/dy/world/20080327TDY01301.htm
From this article I want to highlight some of the ideas presented:
"Recent riots in Tibet ahead of the Beijing Olympics and a change of administration for the first time in eight years in Taiwan could significantly change the status quo in China. These two incidents present the international community with the question of how to cope with China--a nation that has rapidly grown into a military and economic power, while also ruling its people with an iron fist."
How to deal with China is indeed a great question and given the history of the U.S. and its foreign policy making it is not out of the question to think that the PTB would want some military strategies in place in case of a falling out with China.
"maintaining peace and stability across the Taiwan Strait would continue to be highly important for the United States."
"As Bush reiterated in the statement, Washington wants Taiwan to refrain from unilateral action to change its relationship with mainland China or challenge the principle of one China. In short, the United States wishes to maintain the status quo."
The U.S. most likely would not like it if Taiwan were to negotiate peace with China on its own because it removes a strategic ally from the grasp of the U.S. if they do. The stability of the region has nothing to do with benefiting Taiwan as much as it has to do with the U.S. and its need to have control and a strategic geographic location.
Why do we need to have a strategic ally?
"The U.S. economy faces a 400 billion dollars fiscal deficit and defaults on subprime loans (housing loans to low-income earners). It is now partly supported by investment from China, including the purchase of U.S. Treasury bonds by the country, which now has the world's largest foreign currency reserves."
There are certainly other issues that make the U.S. quiver and would give the PTB reason to hedge its bets.
"Of course, the United States also feels increasing concern that China will become its biggest competitor, both economically and militarily."
Finally from this article the following statement gives as much reason as any as to why the U.S. would want Taiwan to be aware of nuclear technologies.
"Paul Krugman, a U.S. economist, has pointed out that China has become too big to bully. In the changing relationship between the United States and China, the priority for U.S. diplomatic policy is deviating from pursuing ideals such as human rights and freedom of religion."
This may only be the tip of the iceberg and definitely could be ferreted out more but it certainly is a start.