Although the "intellectual puppets" line can be read as indicating a certain respect for the Vulcans even now - which would fit with the sense that, even if they've retreated into unfathomable (from a Klingon perspective) pacifism, they remain one of the few Federation races that have almost a semi-respectable standing. Building on historical status as an impenetrable yet inscrutable foe, perhaps. In the Enterprise era, particularly in the novels, it would seem that the Vulcans were able to hold their own against the Klingons to the degree that Vulcan had some manner of diplomatic standing (this comes up in the Augment arc, for instance); no doubt the Klingons tested Vulcan combat ability in the past and were convinced that these were no jeghpu'wI. In the Errand of... books, if I recall, it's still the case that Vulcans are considered more able to reach out to the Klingons than most. It would seem that by the time of The Voyage Home the Vulcans are being dismissed as any legitimate power as Klingons view such matters, but are still (the Klingons believe) trotted out to add some supposed respectability to the Federation's position.
"Oh yes, here comes the Vulcan to be all 'quiet unassuming strength' and logical at us. Not going to fly; we know this is the Human Empire now. Face us directly, Earthers".