The novel explains this more.. Fanucci is set upon by the punks, and later he kills one (presumably.. the guy's found dead). The other one's family pays Fanucci off so he'll forswear his vengeance; Vito at this point realizes Fanucci isn't a real Mafioso, because a real bigshot Mafia guy would kill the second man, not accept money instead.
And suddenly he was sure that Fanucci had no great connections, could not possibly have. Not a man who informed to the police. Not a man who allowed his vengeance to be bought off. A real Mafioso chief would have had the other two men killed also. No. Fanucci had got lucky and killed one man but had known he could not kill the other two after they had been alerted.
....
And so it was Fanucci alone. Or Fanucci with some gunmen hired for special jobs on a strictly cash basis.
So he knew that Fanucci was just bluffing about having Maranzala's permission to collect. This was, of course, proven since nobody ever came after or took over the Fanucci rackets.
The book further hints/explains that Fanucci was so feared because most of the people who paid him were elderly or had no male children to protect them; it even makes a quote about it:
[Fanucci] was reputed to be of the "Black Hand", an offshoot of the Mafia which extorted money from families and storekeepers by threat of physical violence. However, since most of the inhabitants of the neighborhood were violent themselves, Fanucci's threats of bodily harm were effective only with elderly couples without male children to defend them. Some of the storekeepers paid him trifling sums as a matter of convenience.
