Probably true, though as Gandalf himself refers to Treebeard as old.
In Chapter 5 of The Two Towers, Gandalf calls Treebeard "...the oldest living thing that still walks beneath the Sun upon this Middle-earth." In The Return of the King, Chapter 6, "Many Partings", Celeborn addresses Treebeard as "Eldest."
If Maia are included, then Sauron and Radagast (if still alive) would be just as old.
