I really liked how he killed him, too. "Fabrizzio, Michael Corleone sends his regards." I love when gangsters say that before they kill someone. It's awesome!
Sure, it made for a very satisfying passage. But, in real life, it would have been a grave mistake for Michael to have told a button man that he--Michael--was behind the killing the button man was ordered to do. If that happened, the button man could have been in a position to testify against Michael if he'd been arrested and the cops had squeezed him. Most likely, someone far down the chain from Michael would have told him, "Kill this Fabrizzio guy, and don't ask any questions."
