Greene was talking to Barzini Roth and Ola were unknown in Godfather, popped up in II like Pentangeli
Business was Greene running the Hotel the Corleones bankrolled

the great Don Corleone's son was banging cocktail waitresses two at a time! and was slapped around in public

It is possible their paths never crossed until Ola bumped into Fredo in Beverly Hills and gives the dirt on Roth's plans to conspire against his brother, for something in it for him