I think it a Corleone family's strategy to make themselves look weak before their enemies.
Vito,by giving money to Fanuci,makes him believe that he had no "bad intentions" against him,that's why Fanuci walks around alone,careless.
The alibi assumption is ont right:It's NY in '20s-noone gets arrested:)
What the film doesn't clear however,is what was the reaction by the Fanuci's bosses.Clemenza says that the neibourhood was "given" to Fanuci by the "Black Hand" or something.No reaction by the organization however...