And Saruman became evil and greedy for the One only quite late, perhaps even after Sauron's cover was blown (or at the most a few decades before). According to Appendix B, Sauron's identity is exposed in TA 2850 and Saruman begins to search the Gladden Fields in secret for the One the year after that. Probably he has already been toying with the idea of getting the One for himself earlier. We have to remember that the very popular and lasting image of Saruman as an evil schemer and adversary of the Free Peoples is a relative recent phenomenon in the tale of years of the Third Age. For about 1,700 years he was a loyal, resourceful and steadfast ally of the Free People in their struggle against the Shadow! His tragedy began only quite late in his career. He took Isengard for himself in TA 2759 and at first he was probaly a loyal ally, turning to evil ideas sometime in - IMHO - later years of the second half of the 28th century TA.Mim wrote:Tolwen summarizes it well by noting that the Enemy beguiled or misled the Wise. In addition, Saruman's treason threw them off the track for a bit, so to speak.
The one instance where he actively deceives the Wise is when he presumes that he found out that the One had been flushed into the Sea. This happened at the last meeting of the white Council in TA 2953, more than 100 years after Sauron's identity as the Necromancer became known. I guess this is what you originally referred to when talking of Saruman's beguilment
Cheers
Tolwen