“Observable universe” - what’s that, only what we know about?
There is vastly more we DO NOT know, than what we do. The arrogance that somehow Earth is absolutely unique is unfounded by any empirical knowledge we now have.
Sheer distance alone would make the probability of actually knowing if there were any other life forms out there purely conjectural, but that does not mean that some other advanced society may have already solved the twin paradoxes of instantaneous travel between points of the Universe, and the time displacement of achieving that instantaneous transport.
“Where are they?” —Enrico Fermi
Nothing suggests that the scientists' aim was to somehow show that Earth was special. The intent was to do the math and show the probability of other intelligent life forms.
It seems like a big improvement over the Drake Equation. And it is a methodology that could generate different results if/when the probability distributions they use as inputs are modified.
Talk about arrogance! Where is this empirical knowledge you claim we have?
We have exactly one data point: Earth.
Furthermore, it is the height of inanity to presume by observation they mean see with a telescope.