In the meantime, here's my explanation....
There's a big difference between rolling an aircraft and flying it inverted for an extensive period. ANY aircraft can roll if the pilot is good enough and there is enough altitude. A properly executed aileron roll is a 1G maneuver all the way around, something many people miss. Ask any aerobatic pilot.
As demonstration, here's Bob Hoover doing it, and EddieC has already posted a link to Tex Johnson rolling the B707.
(notice how much he has to pitch up before rolling so as to not be in a vertical dive after losing so much altitude in the roll)
However extended negative-G flight, i.e. any flight attitude where the airframe is "unloaded," is not possible in all airplanes. The engines are usually the limiter here (jets flame out, props just sputter and quit from fuel and oil starvation).
Beyond the engines, the wings and elevator authority are the limiters. Since wings create lift best when the curved side is on the top, and most aircraft have a flat-bottomed airfoil to some degree, it requires a LOT of down elevator (forward stick) to create enough angle-of-attack to create enough lift to support the airplane when inverted and the flat side is on top. This is why aerobatic planes have symmetrical airfoils. Do some quick Googling on the differences between the flat bottomed Citabria and Pitts S1-C versus the symmetrical Decathlon and Pitts S1-S.
In the case of the Decathlon, it sacrifices climb performance because of the extra drag, but completely outperforms the Citabria in inverted flight (some say it climbs equally well inverted, but I can't verify that anywhere).
So to sum it up, since the engine flamed out in the movie (I think?), it comes down to whether or not the MD-83 has enough elevator authority to maintain a reasonable descent rate, let alone level inverted flight. Personally, I highly doubt the MD-83 has what it takes, but I'll let those who have actually flown it speak.
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Flight (2012 film) - Can airliners fly inverted? - 
I'll wait for the netflix release. I got to meet a B-17 ball turret gunner who plane was shot down over france on his 2nd mission. He survived the initial attack of a 190 and after climbing out of his turret wounded he found most of the crew dead, and then the plane rolled over and the tail snapped off. He managed to crawl his way to the tail and open his chute and throw it out the hole and was pulled from the plane, barely 1000 ft from the ground. He broke his ankle on impact but survived the rest of the war as a POW. In the 1980's he met the German pilot who shot him down. Now that's a story that would make a great movie.
The Captain probably has forgotten. 
