Did Saruman Believe He Could Master The One Ring?

[the phantom]

Think what you will about how much Sauron could see, Fordy, but it is a fact that Sauron's powers/abilities are lesser when using the palantir.

In letter 246 Tolkien says that Aragorn could not have withheld the Ring from Sauron if face to face, and continues on to explain how he was able to "win" the palantir contest despite that.

In the contest with the Palantir Aragorn was the rightful owner. Also the contest took place at a distance, and in a tale which allows the incarnation of great spirits in a physical and destructible form their power must be far greater when actually physically present.

Sauron wasn't the rightful owner, so he couldn't wield the palantir perfectly. And on top of that his powers, which would include powers of perception, were greatly dimmed by distance.

I think you should've just stuck with the phone analogy you were using at first. Do you think Sauron could've told the voices of Pippin and Frodo apart on the phone having never heard them before? And really, do you think he could've picked their faces out of a lineup? In person, yes, but just from a photo where there is no physical presence involved? I doubt it. The Nazgul weren't equipped with digital cameras as far as I know.