Odd Conclusions in Reference to Age and Fallibility

[Feanor of the Peredhil]

As I was reading The Two Towers today, I came across an interesting line:

"Treebeard is Fangorn, the guardian of the forest; he is the oldest of the Ents, the oldest living thing that still walks beneath the Sun upon this Middle Earth." ~Gandalf the White to Aragorn, Legolas, and Gimli.

Now, when I read this, I remembered another line in The Fellowship:

"Eldest, that's what I am. Mark my words, my friends: Tom was here before the river and the trees;" ~Tom Bombadil.

And also:

"Iarwain Ben-adar we called him, oldest and fatherless." ~Elrond Halfelven.

These statements conflict quite nicely, confusing me as to who is older: Bombadil or Fangorn. Now Bombadil himself tells us that he is oldest, and Elrond Loremaster agrees, however Gandalf, as the White, claims that Fangorn is the oldest living thing that walks ME.

This statement can be taken a few different ways, that I can think of:

1) Fangorn is older than Bombadil.

2) Bombadil is not actually a living thing.

3) Bombadil doesn't walk: he dances, or some other nonsense technicality.

or:

4) Gandalf is simply wrong.

Since I'm stuck on this, and I could very well be missing an interesting tidbit of information, I'd like some thoughts on this. Or possibly links, but I don't think you'll find any of those, since I looked for quite some time for a thread discussing this particularity.

Fea