My "Duh" moment.
Plutonium is not just in the MOX (Mixed Oxide) fuels that are used in the Reactor No.3. It is in the Reactor Pressure Vessels, and it is in the spent fuels stored (I hope) in the pools above (I hope) the Reactors No.1, 2, 3, 4.
Why? Because plutonium is a byproduct of uranium fission. Duh.
From World Nuclear Association's paper on Plutonium:
In practical terms, there are two different kinds of plutonium to be considered: reactor-grade and weapons-grade. The first is recovered as a by-product of typical used fuel from a nuclear reactor, after the fuel has been irradiated ('burned') for about three years. The second is made specially for the military purpose, and is recovered from uranium fuel that has been irradiated for only 2-3 months in a plutonium production reactor. The two kinds differ in their isotopic composition but must both be regarded as a potential proliferation risk, and managed accordingly.
Plutonium, both that routinely made in power reactors and that from dismantled nuclear weapons, is a valuable energy source when integrated into the nuclear fuel cycle. In a conventional nuclear reactor, one kilogram of Pu-239 can produce sufficient heat to generate nearly 10 million kilowatt-hours of electricity.Plutonium and nuclear power
Plutonium is formed in nuclear power reactors from uranium. When operating, a typical 1000 MWe [megawatt electrical] nuclear power reactor contains within its uranium fuel load several hundred kilograms of plutonium.
So far, after more than 2 weeks since the first explosion (Reactor No.1) occurred, Fukushima I Nuclear Plant seems to have quieted down. Move on, nothing to see here.
It is possible that they are not telling us, but no, Japanese people are honest and hard-working, right? Right.