Of Domination and Tools

[Inziladun]

The chapter in Unfinished Tales, The Palantíri, goes into some detail of the nature of the Stones, and the means by which Sauron was able to use them against Denethor and Saruman. It is said that the Minas Anor Stone was more amenable to Denethor as a legitimate ruler of Gondor, though Sauron's power and will were greatest of the three.
What's interesting is a striking similarity of apparent thought and even verbiage concerning Gandalf, from Saruman and Denethor.

Denethor said to Gandalf:

'Pride would be folly that disdained help and counsel at need; but you deal out such gifts according to your own designs. Yet the Lord of Gondor is not to be made the tool of other men's purposes, however worthy.'

ROTK Minas Tirith

And later:

'But I say to thee, Gandalf Mithrandir, I will not be thy tool!'

The Pyre of Denethor

When the hobbits confront Saruman at Bag End, he mocks their trust in Gandalf, saying:

'When his tools have done their task he drops them.'

The Scouring of the Shire

So it seems both Saruman and Denethor had the idea that trusting Gandalf would mean they were his "tools", which he would use for his own ends. Now, where did that originate? Denethor, or Saruman? Or Sauron? Did he implant that into both their minds, as a move against Gandalf?