Given that parts of the Trilogy are based on a version of real-time events, that statement may have been a reference to a Bonanno family member that died of a heart attack. I believe that Joe Magliocco who succeeded Joe Profaci died of a heart attack also.
While much of the films were based on real life events, they aren't completely historically correct. FFC took editorial liberties where he saw fit. If Clemenza died of natural causes, the dialogue would have ended there, but since Willie Cicci added, "that was no heart attack", it leads us to believe that very possibly Clemenza death was something more then a "real" heart attack.
