We are not Communists/Bonasera also
Solozzo wanted access to Vito's influence. Vito refused this. But had not other families over the years asked for such help?
Or was the Turk's request the very first time after 20 years or so of Vito being in such a position that anyone had thought to ask for Vito's help and he turned them down?
And Barzini showed he was connected with the Turk clearly by his little quip.
Also, had Bonasera gone to Vito before the trial, perhaps the scoundrels who beat his daughter wd have been serving long sentences -- I guess the undertaker did not think it necessary.
Note: I think as others have said that Vito did in fact share his judges; Barzini then was saying, no matter what, you always have to provide this service even if you think it will compromise your (Vito's) relationship with the judges. This unreasonable position is perhaps in part why Barzini needed to go, even without his role in Santino's death.
I wonder if Barzini was at the wedding out of genuine friendship or because Familes' members socialized with other members or "keeping enemies closer" -- perhaps that early scene was supposed to come back to the viewer when Michael says it. Also, Geary was quite an example of that. A man Michael had to have despised; but after the brothel incident, they were very close indeed.