lol
Your asking the correct person
It's actually Genco, Vito's friend (later his consigliere), who says that Fanucci is Black Hand
It's debateable whether Fanucci was actually "Black Hand"
- As you mentioned Vito says "Joe the Greek on Tessimo Avenue, Frank Pennitanlo, and Tachinko Schrabo. They don't pay Fanucci."
-Fanucci never has bodyguards, and is attacked by street punks
-When Vito tries to negotiate, Fanucci says something along the lines of : "If you refuse, the police will come and you'll be arrested"
-He accepts Vito lesser amount of money
- There are no reprisals to his assassination
None of the above would have occurred if Fanucci was Black Hand
So I believe Fanucci is just the neighborhood bully and has no real connection to the Black Hand/La Cosa Nostra/Mafia.