It’s often pointed out in the international relations literature that the notion “puppet” is not a simple one. Puppets can often influence the dominant power significantly. The Soviet satellites were certainly “puppets,” if the term has any meaning. But unlike Western powers, Russia subsidized its satellites massively, to the extent that they were mostly richer than the mother country itself. Not out of deep human sympathy, but for straight power reasons.
Same in this case. I can’t really expand on the statement you quote without running through the history since the 1930s. I’ve discussed a little of it in print, and there’s a great deal more literature on it, but I can’t try to review it here.
Up to the highest levels of the US government (Wolfowitz for one,
explicitly) it’s understood that US bases in Saudi Arabia were a major rallying cry (probably quite sincere) for bin Laden. That’s why they’ve been downgraded.
The Saudis have some freedom of action. The same is true of subordinates, even local store owners, in a Mafia-controlled system. If they go too far, they’ll get in trouble. Furthermore, their own interests are closely aligned with Western (primarily US) power. They don’t represent their own populations, after all.
Since the 1950s, it’s been clear enough — even explicit in high-level US internal documents — that the people of the region bitterly resent US support for corrupt and brutal ruling groups and US opposition to democracy and development.
There’s no doubt that al-Qaeda regards the Saudi rulers as one of its chief enemies, maybe the prime enemy. But that does not imply that elements within those ruling circles refrain from exploiting al-Qaeda-style organizations for their own purposes. The US was hardly pro-Nazi after World War II, but happily used some of the worst Nazi war criminals for its own purposes.