There are at least two interpretations of probability. Firstly the epistemological, as you say, represents our lack of knowledge about the world. Secondly the aleatory truly represents the phenomenon of chance in the world.
The best interpretation of quantum theory for example (as I understand it) takes the latter view that randomness is genuinely physically manifested, and does not simply represent our inability to model reality.
I think you're confusing concepts. The original point is about the difference between the map and the territory. And, because I'm (finally) systematically going through Eliezer's sequences: http://wiki.lesswrong.com/wiki/Map_and_Territory_(sequence)
Your second paragraph is about a particular map: quantum theory. Quantum theory has probabilities in it. The dominant interpretation of quantum theory is that the probabilities accurately represent what happens in the universe; they are not artifacts for us to correct. But there is still a difference between our map (quantum theory) and the territory (the universe itself).
Put another way: quantum theory is a map with uncertainty baked into it. But this uncertainty has been accurately mapped.
No I don't think so. Unlike statistical physics, where probabilities are simply a mathematical technique for dealing with uncertainty, quantum mechanics actually postulates that randomness is inherent to the universe.
If you disagree with me, please describe how your concept of "maps and territories" applies to the StatPhys/QM distinction.
Suppose I accurately map the coastline, and every relevant part of the coastline is depicted in my map. But the map is not the same as the coastline itself.
If my coastline has some feature that blips in and out of existence in a predictable way, I can integrate that into my map. My map then has uncertainty in it. That uncertainty is an accurate reflection of the coastline itself - but there is still a distinction between the map and the coastline.
I don't disagree with your second sentence. But there is still a difference between our theory of quantum mechanics and the universe itself.
The best interpretation of quantum theory [..] takes the [..] view that
randomness is genuinely physically manifested
We could argue endlessly about whether that is 'the best' interpretation (which ethical assumptions does your 'the best' presuppose?) but fortunately it doesn't matter. As Mermin (from the famous Ashcroft and Mermin book on Solid State Physics) famously quipped: you can 'shut up and calculate'. The usefulness of the model does not depend on its interpretations (although the interpretations are certainly important with respect to scientific progress).
The best interpretation of quantum theory for example (as I understand it) takes the latter view that randomness is genuinely physically manifested, and does not simply represent our inability to model reality.