To return to the original discussion, I think there could also be a possibily that Don Altobello may have been a member of the Bocchiccio family.

This correlates with his ties to Sicily ("keeping the peace between Palermo and New York" as Don Tommasino stated) and "as the family's oldest friend he was always chosen to bring messages".

In the novel, the Bocchiccios are known as mediators just as Don Altobello appears as one in Part III. It is him who sets up the meeting with the other bosses just as the Bocchiccios organized the meeting of the Dons in Part I.

If he wasn't a member of the Corleone family, the Bocchichios are the only other New York family I could see him being a member of and at the same time being extremely close to the Corleones.