My point here isn't (ahem) "You are wrong.", but more that I think you need to get some perspective about the distinction between strongly held opinion and objective fact.
https://implicit.harvard.edu/implicit/user/agg/blindspot/tab...
I went back and checked the Medium website with a handful of different typefaces on the body text, and whilst I could tell a large difference in readability between the default (ff-tisa-web-pro?) and my systems DejaVu Sans, I honestly couldn't tell the difference the default and Georgia (serif) (screenshots in another comment below).
Which brings me back to my point, that the typeface is highly overrated in importance on a page. The choice of font-size, Sans/Serif, line-height/width, etc. all play a far more important role when it comes to readability.
I will admit that I do come from a strong science/programming background, so sometimes the more arty, design side of things escape me!
Even if you cannot readily quantify the difference between, say, Roboto and Source Sans, the difference is there and your perception of either is different. The difference might be slight, but it is sufficient to skew your "2 second" impression in the wrong (or the right) direction. For example, even though Roboto and SS are almost the same typeface, Roboto in regular weight renders much heavier than Source Sans, so if you are to use for a product that is meant to exude lightness and airness, it would work worse than if you were to use SS.
Things like overall feel and the "rhythm" of a typeface take an effort to notice, quantify and rationalize, but they are of an UTMOST perceptive importance. Ever noticed the quirky lowercase "a" in Proxima Nova? Ever noticed how that "a" just steals the show if it appears in a sizes larger than 16px? No? Just pay closer attention next time ;) The same goes for HF&J's Whitney - it looks like just another sans-serif font on the surface, but it just feels friendlier. Try and quantify that (Kotaku uses it, go check it out).
First impression is hugely important and a typeface choice plays a very big part in it. Don't make a mistake of underestimating it.