Treebeard the wise?

[Inziladun]

Or Treebeard simply did not know Saruman was a Maia, and assumed he was born sometime late Second or early Third Age only.

I would think that the most likely. Treebeard did have a lot of wisdom, but he wasn't all knowing. On the other hand, he seemed to be on very good terms with Gandalf. Did Gandalf keep his origin secret from Treebeard? If so, why? If not, why wouldn't Treebeard know Saruman was a creature of the same order?