Yes. I believe that is true.
Like I said, Saudi politics is not for the feint of heart. The rationale for this apparent dichotomy may be that the Royals and the Mullah's are supporting different factions. But that's just a guess.
The other possibility is that the Saudis would suffer greatly if there is a major disruption in their ability to supply oil and collect dollars in return. Wars tend to disrupt that sort of thing which is why the Saudis, while being driven by their Wahabbi beliefs, would still favor stability over allegiance to Allah.