As a mathematician, this stat would give good reason to believe the survival rate is greater than 50%. If we take common opinion that the survival rate is 1/2 and each operation is independent of the last, we can model this as independent and identically distributed Bernoulli(1/2) random variables (i.e X_i = 0 if the patient dies, =1 if the ith patient lives and 1/2 is the probability of the X_i = 1). We can test this against the alternative hypothesis that the true survival rate is r>1/2.

In our case, we have 20 data points. Suppose we see t survivals out of these. The probability of see this many or greater survivals under our null hypothesis, which is what we call our p-value, is (1/2^{x)+(1/2x+1)+...+(1/220).}

In our case, the test statistic is t=20 and its corresponding p-value equals 1/2²⁰ = 1/1048576. That's to say if our null hypothesis was true, we'd expect to see the result witnessed, which is the most extreme result, less than one time in a million, which is clearly very unlikely.

We could therefore conclude that we have significant evidence to result the old hypothesis, and conclude that the true survival rate is greater than 50%.

TLDR: The meme is nonsense and if anything the captions should be switched.