The paper doesn't explain anything at all. If we are alone in the galaxy - it tells us absolutely nothing about why this is the case, and certainly not that it's unrelated to the factors in the Drake equation, as you seem to claim. On the contrary - the "explanation" it offers relies precisely on the assumption that the factors of the Drake equation are responsible. The only thing it says is that we should incorporate our uncertainty of them when trying to make an estimate. It might be interesting, but it adds absolutely nothing new about why we might be alone, other than "because some factors could be lower than we think". Duh.
The paper exactly explains why this is not the case. This is demonstrated using undergraduate level Bayesian probability.
This response is one of many when this work comes up on HN that would benefit from a basic understanding of multivariate probability.