Saruman taking ring from Gandalf..

[Gorthol]

But the Red Ring remained hidden until the end, and none save Elrond and Galadriel and Círdan knew to whom it had been committed.

This is contradicting my citat from Unfinished Tales above, could you please explain this Lord of Angmar? Could it be so, that the statement in Silmarillion (the one you gave) means that no one of the "ordinary" people of ME i.e. elves, men, dwarves, etc.. did know who wore it, but Saruman is excluded from these?