The explanation, I am sorry to say, is incorrect. Only a tiny fraction of the fissional material is “used up” (converted into energy) in an atomic bomb, over 99% survives intact.
I guess we could argue over whether 2% is a tiny fraction or not. Certainly there was enough used up to destroy both Hiroshima and Nagasaki. That which wasn't used up was wasted and modern weapon design attempts to maximize that percentage.
Perhaps you can help by providing an estimate of how much plutonium exists today at Fukishima. If I am correct that at least one of the reactors was plutonium based, and given that spent fuel from that reactor may also have been on site, how much plutonium is there and how does it compare to the amount of plutonium used in the Nagasaki bomb?
I would be very surprised if the amount of plutonium present at Fukishima isn't much greater than that used in the Nagasaki bomb. Perhaps you will surprise me.
I will certainly admit that the internet today has much, much more detailed information about these subjects than when I was in college in the sixties.