Someone once told me how they pulled an uncirculated coin out of a roll. How can it be so if it was in a mixed roll?
Uh, I have found several proofs in rolls. It does happen. Of course most of the time the proofs are damaged, but occasionally you will turn up a decent find - I got a nice '77-S Ike the other day at one of my banks. And I have found BU or nearly BU nickels from the 1940's, with all original mint bloom. Someone cracked a roll and put it into a coin machine.
One of my co workers got a 1949d quarter in change at Sonic and I sent it in to ANACS with my last order for him and it came back ms63 and is as white as snow. (his first ever slabbed coin.)
I think the issue you are having here is an inaccurate definition of uncirculated. While literally it would indeed mean that the coin has never seen circulation (making finding one in a mixed roll impossible), the accepted definition for a coin grading uncirculated is that there is no wear on the coin. This is indeed possible in a mixed roll if the coin has managed to avoid excessive human contact.