You just opened up a big can of worms.

Treebeard did indeed claim to be "the oldest living thing that still walks beneath the sun."

However, Tolkien himself said that "Treebeard is a character in my story, not me; and though he has a great memory and some earthy wisdom, he is not one of the Wise, and there is quite a lot he does not know or understand..."

Gandalf did indeed call Tom the oldest thing on middle earth...

And treebeard did say he himself was the oldest living thing on middle earth...

Could Tom be one of the Vala or Maia?