The only thing the fermi thingy shows, is, that there is not an expanding colonizing tech civ near to us in time and space to have colonized us. It is neither a contradiction nor a paradoxon.
The name is Fermi Paradox, so yes, there's indeed a paradox, and no it does not talk about expanding colonizing tech civ., it's way more flexible than that, it talks about any evidence of any (human comparable) intelligent life at any given past time, and yet we haven't found any, which contracts to your math, because you said 1% per galaxy, earth is only 0.00000000001% of the milky way so where are all the other 0.99999...% of intelligent life in our galaxy? We haven't found, thus the paradox.
I never said we're probably alone, I said we don't know if we are alone or not, thus things we know for sure are more scary, like us destroying our own planet.