> That's insanely accurate.

This is misleading, and it's a misconception arising from the way that even physicists sometimes misspeak when talking about statistics. The "sigma" is a reference to a standard deviation, and we use it to measure evidence against a null hypothesis (which is generally defined relative to a model of some type). An 11 sigma result means that there's strong evidence against (hypothesis + model), not anything in absolute terms about "accuracy".

The meaning of such a result depends on the model being used; sometimes it's as simple and easy to defend as there being some sort of distribution with a mean which exists, and other times there's a complicated model which may itself be incorrect (producing significant results).