I'm still not convinced about exactly what Murder Inc is. It seems to be remnants of the Bug and Meyer Mob, the then-current Buchalter gang, and the aforementioned two Italians. But were they an organized killing squad taking marching orders from the governmental body known as The Commission? There are so many erroneous reports surrounding the Inc, and so much media sensationalism during their heyday, that whatever happened is best left to the historians. Unfortunately, in older mob lore it becomes unclear exactly what is myth (The Last Testament of Lucky Luciano) half-truth (the Commission controlling OC rather than arbitrating it) or hard to believe, but true (Pittsburgh Strauss' killing hundreds of people). Anyone want to take their best guess?

I too wondered if Parisi was made. He fled New York in 1949 and Albert, his patron, took over two years later, but there's no reason to believe Albert couldn't propose him for membership, unless working for Murder Inc. makes you ineligible for made status, which seems pretty hard to believe. Here's a story about an old murder Parisi and Anastasia were both involved in. It says he was collecting union kickbacks in the prime of Mangano territory as far back as 1939. The article is a bit long, so use command F on a mac or ctrl f on windows, and type "parisi".
http://www.transportworkers.org/node/1618