Why didn't Galadriel warn Aragorn that Boromir wanted the Ring?

[Inziladun]

Thinking on this, maybe it's possible Galadriel didn't know exactly what was on Boromir's mind. When Gandalf the White meets Aragorn, Legolas, and Gimli, he says Galadriel warned him Boromir was in peril. That's fairly vague.
Boromir himself said of his experience with Galadriel's "trial", that

'....it seemed exceedingly strange. Maybe it was only a test, and she thought to read our thoughts for her own good purpose; but almost I should have said that she was tempting us, and offering what she pretended to have the power to give. It need not be said that I refused to listen. The Men of Minas Tirith are true to their word.'

FOTR The Mirror of Galadriel

Why would Galadriel be "offering" the Ring? It was not in her possession, and Boromir would not have felt her permission to use it necessary. And what word would Boromir have been breaking by taking the Ring? Elrond specifically said at Rivendell that only Frodo was held to an oath in relation to the Quest. Perhaps Galadriel divined a more general lust for power to defeat Sauron, coupled with a desire to have Aragorn out of the way and rule Gondor himself. After all, I doubt Galadriel could literally read minds. The test of the Fellowship seems more like a overall sensing of the target's emotional state, in response to Galadriel's selective "temptations".