Quick note: Fermi's Paradox isn't a scientific rule, only an observation based on early speculation (ie no data).
I don't have access to the paper this article is based on, but in reading the abstract even the authors point out that this calculation makes many assumptions, and that has always been the crux of these types of predictions. When Frank Drake came up with the Drake Equation, we didn't even know what values to plug into many of the terms in that equation. Since then we've learned so much more about how solar systems form, and have discovered thousands of exoplanets that allow us to make semi-reasonable statistical statements.
Ultimately, it's still too difficult to accurately predict the existence of exo-civilization because we're still basing too much on our single sample of one known civilization: us. We can predict how many planets probably orbit stars in their Habitable Zone, but that alone does not mean life (let alone intelligent life) will arise there. More importantly, even if only a tiny percentage of those billions of planets in our galaxy alone lead to intelligent life developing into civilizations, the time factor really messes any reasonable chance of co-existence with us.
There's every reason to believe that civilizations (as a whole), when plotted along a Time axis, rise and fall. It could be a normal distribution with a very even gaussian (bell) curve, so while some would end abruptly for a number of reasons, all would start out small and grow, then eventually shrink and fade. And here's the trick with this case: you could have 36 civilizations arise in the Milky Way, but none of them probably exist at the same time, so their curves never overlap.
And on top of that, our galaxy is about 100,000 light years in diameter. We're located out in the suburbs of the Orion Arm, and if another civilization was on the opposite side of the galaxy we'd likely never know. Even if both civilizations last for exceptionally long times, in the cosmic sense it's just a blink of an eye.
So is it possible that there are 36 other alien civilizations in our galaxy right now? Yes, it's possible, but it's highly unlikely.
www.forbes.com 
