What exactly do [the authors] mean by a quantum state being “statistically interpretable”?... Basically, [the authors] call something “statistical” if two people, who live in the same universe but have different information, could rationally disagree about it.... As for what “rational” means, all we’ll need to know is that a rational person can never assign a probability of 0 to something that will actually happen.
To illustrate, suppose a coin is flipped, and you (but not I) get a tip from a reliable source that the coin probably landed heads. Then you and I will describe the coin using different probability distributions, but neither of us will be “wrong” or “irrational”, given the information we have.
That's Scott Aaronson discussing a paper about the nature of quantum states. Googling "define statistical," I see, unsurprisingly, "of or relating to the use of statistics," and then googling "define statistics," I see "the practice or science of collecting and analyzing numerical data in large quantities."
To me, the large quantities bit emphasizes that the role of statistics is to parse signal from noise, which is only possible with more than two data points (or, to be fair, some assumptions). So, I'd consider the authors' use of the word statistical to be sort of non-standard, because it seems to be able to be used for interpreting just one quantum state.
Quite possibly this is actually standard use of the word statistical among certain physicists, which would make this yet another example of why you shouldn't assume that terminology is at all consistent across disciplines.