Is OpenAir "True Cloud"?

Yes. OpenAir is, and has always been, a cloud solution. This means more than just being hosted: OpenAir is configurable, can be changed over time to adapt to your changing business processes, all customers are on the same version and all customer are upgraded at the same time. Additionally, all customers get access to all new features the day they are available. Be cautious of any vendor who locks you into a version or upgrades each customer one-at-a-time.