I'm the one that created the graphic, though as noted in the accompanying post it's not originally my insight. Let me provide some context for how it came up and do my best to explain how I understand it. The realization occurred during a discussion with a student who had mostly learned the Bayesian approach to inference up to that point. He was having a hard time understanding the whole hypothesis testing paradigm, and I was doing my best to explain this decidedly confusing approach (if you consider “difference” to be a negative - as in not equal to - then the standard null hypothesis approach is a triple negative: the researchers’ goal is to show that there is not no difference). In general, and as stated in another response, the researchers usually expect some difference to exist; what they really hope to find is convincing evidence to “reject” the null. To be unbiased, though, they begin by essentially feigning ignorance, as in, “Well, maybe this drug has zero effect on people.” Then they proceed to demonstrate through data collection and analysis (if they can), that this null hypothesis, given the data, was a bad assumption.
To a Bayesian, this must seem like a convoluted starting point. Why not just begin by announcing your prior beliefs directly, and be clear about what you are (and aren't) assuming by encoding it in a prior? A key point here is that a uniform prior is not the same as an uninformative prior. If I toss a coin 1000 times and get 500 heads, my new prior assigns equal (uniform) weight to both heads and tails, but its distribution curve is very steep. I am encoding additional information that is highly informative! A true uninformative prior (taken to the limit) would carry no weight at all. It means, in effect, starting from scratch and, to use a frequentist expression, let the data speak for itself. The observation made by "Clarence" was that the frequentist way to encode this lack of info is with the null hypothesis. It’s not exactly the same as an uninformative prior; it's the frequentist approach to expressing maximal ignorance in an honest way, one that doesn't presume what you wish to prove.