It's not a secret from the chemical point of view. However it takes specific technologies to manufacture a functioning battery out of basic chemicals. Most OEM batteries in laptops come from Japan. Batteries are wearable parts, so having a battery plant guarantees you a lot of repeat business.
Also A123 was working on improving the technology. This is particularly important in light of those fires on 787. Not every battery is good enough to operate in a vehicle that experiences serious high frequency vibration. Yes, the chemistry is dangerous. But it offers the most energy density among rechargeable batteries (especially per unit of weight.) Better batteries will be even more dangerous; if you want your laptop to work for weeks the battery has to hold all that energy, and if all that energy is released quickly you will get fire or explosion. Reactions that can hold lots of energy are also capable of quick release of it. Reactions that are slow and safe are also not very capable (Ni-Cd, Alkaline.) Prius batteries use NiMH, it is somewhere in the middle - not very capable, but very safe. The plug-in Prius uses Li-Ion, but I only read about such a car; I'm unsure if it exists.
Nonetheless, isn't the entire objection here to the Chinese buying anything in the U.S.?
I don't know. They are welcome to buy many things that we make for sale, or that we plenty of, or that we don't need. The money must flow both ways. But, as usual, you have to be careful what you sell and to who. Aims of China are very well known - to become the dominating force on the planet; and Chinese rulers were never too gentle with their subjects.
That is very true -- I'm no apologist for China's political system. Trade, though, is still a very effective peacekeeper.