Have another bong hit. A cessna 172 will fly all day inverted, providing power or a steep glide. A positively cambered wing will produce lift inverted. How is it that my slow stick park flyer with an undercambered wing will fly inverted? with or without power? Not the most efficient arrangement, but it works fine. I have flown inverted in many aircraft, full size & model, without symmetrical airfoils. You are wrong, go take a basic ground school.
A full size heli has a small amount of negative pitch available to autorotate, either at the head, or through twist on the blades, otherwise, the rotor would not spin due to air flowing upwards through the rotor disk, (unpowered decent) and autorotation would be impossible.
Full size heli's will not fly inverted for several reasons. If it has a teetering rotor head, it MUST remain loaded at positive G, or it will mast bump (look it up) as far as the rest, assuming the fuel & lubrication systems were designed for inverted,
the blades are too flexible to prevent hitting the tail boom from abrupt control inputs. Model heli's blades are relatively stiffer. If a full size heli were designed the same as the model and scaled up, everything else being equal, they would indeed be capable of inverted flight. Problem is, if it doesn't work or you screw up, you can't jump out. Who wants to try it first?
There has been an aerobatic heli team performing for years with 3 R-22 helis out of Salinas, Ca. called "the showcopters". They have been performing at airshows for years. (no inverted flight). They are remarkable to anyone aware of the limitations of a teetering rotor system. One of them was killed a few years ago when one of there students made an abrupt control input. Blades came off, struck fusalage, R-22 fell down, fire consumed everything.
Rest in peace Kent.

-Dan