
Sorry, but Tolkien did not say what you just wrote. Gimli said it and he has been known to be wrong about many such things.
and later Gimili asks Gandalf about the encounter in the same chapter,from The Two Towers, The White Rider
...'That would not baffle a Ranger,' said Gimli. 'A bent blade is enough
for Aragorn to read. But I do not expect him to find any traces. It was an evil phantom of Saruman that we saw last night. I am sure of it, even under the light of morning. His eyes are looking out on us from Fangorn even now, maybe.'
Now exactly which part of what the author says do you want us to believe?'Wait a minute!' cried Gimli. 'There is another thing that I should like to know first. Was it you, Gandalf, or Saruman that we saw last night?'
'You certainly did not see me,' answered Gandalf, 'therefore I must
guess that you saw Saruman. Evidently we look so much alike that your desire to make an incurable dent in my hat must be excused.'
I guess I didn't make my point very well. The author did not tell us who the Old Man was. He had the characters give their opinions. It could have been Saruman, it could have been Maglor, it could have been Feanor's ghost, it could have been Radagast lost in the woods, it could have been Denethor looking for Boromir.