I admittedly only watched the first 10 minutes or so of The Shocking Truth, but based on this sample size it seems like they just repurposed material from a previous Costello documentary. They mostly talked about Costello's story, then would occasionally place in how it was portrayed in The Godfather.

Costello was Calabrese, and, as even this show points out, was an Americanized, swanky Manhattan guy who lived in a luxury apartment right above central park. Vito Corleone's Sicilian customs and olive oil background resembles Joe Profaci more than Costello. I think Vito's a composite of the two, yet despite the heavy focus on the links between Costello and Corelone, Profaci's name isn't yet mentioned as of the point I watched to.

And, ugh. The reenactments...These are just horrible. Is it cheaper for them to hire these actors and do this than it is to just buy stock footage of 1930s New York the way the Bill Kurtis docs did?