The article and blog's meta-argument involves choosing components over a random distribution of universes and saying "well, there's a good chance you wind-up in a universe with small". But reasoning about random universes is debatable, introducing unnecessary metaphysics but even so, if you wind-up in a universe with a small chance of an advanced civilization, you will wind-up in a universe with Drake's components also small. Which is to say the whole reasoning does nothing but "muddy the waters".
The only way the "randomly chosen universe" argument matters is if we're jumping from universe to universe or if there's a force that inherently keeps us from reasoning about the why of the Drake components - but neither of those conditions are met.
"In this example, the point estimate for each parameter is 0.1, so the product of point estimates is a probability of 1 in a billion. Given a galaxy of 100 billion stars, the expected number of life-bearing stars would be 100, and the probability of all 100 billion events failing to produce intelligent civilizations can be shown to be vanishingly small: 3.7×10 ^−44
[...]
However, the result is extremely different if, rather than using point estimates, we take account of our uncertainty in the parameters by treating each parameter as if it were uniformly drawn from the interval [0, 0.2]. Monte Carlo simulation shows that this actually produces an empty galaxy 21.45 % of the time."
I take this to mean that collapsing a range into a single point will artificially inflate that point, and instead you need to look at the number of possible outcomes, not the average of all outcomes.
From the related blog post:
"Imagine we knew God flipped a coin. If it came up heads, He made 10 billion alien civilization. If it came up tails, He made none besides Earth. Using our one parameter Drake Equation, we determine that on average there should be 5 billion alien civilizations. Since we see zero, that’s quite the paradox, isn’t it?"
That seems like a consistent reading to me. Maybe I'm wrong - I take it you would draw a different conclusion?
Edit: No, thinking about it more and reading some other posts, I kind of get what you're saying. I'm still not really sure I'd call that a paradox though. It still seems to suggest to me that we may not need to rely on any of the really big theories to describe why we don't see life.