Good guys of LOTR clueless?

[dancing spawn of ungoliant]

So once again, it seems Galadriel makes a false claim.

No one, not even one of the Valar, can read the mind of other 'equal beings'

I have to stand up for Galadriel now.
Why would Galadriel had lied she can read some thoughts of Sauron? Maybe to comfort Frodo by making him believe that she knows, what she's doing and Lorien doesn't fall yet. But I don't believe that. Actually, I claim that the quote from Morgoth's Ring (myths transformed, VII, ii) doesn't tell the absolute truth at all (like Legolas already said).
For lo and behold! The Return of the King: book 6: Many Partings:

For they (Celeborn, Galadriel, Elrond and Gandalf) did not move or speak with mouth, looking from mind to mind; and only their shining eyes stirred and kindled as their thoughts went to and fro.

Some people can read many things from other people's faces but not a whole conversation!

In the book it's stated that they (again Celeborn & others) talked about "all the ages that were gone" or they held council concerning next days. Well, I'd think that there was some mind reading involved.