Literally.
Dirt, in the sense of organic topsoil, requires plant life, and often the action of burrowing insects, reptiles, and mammals to form. The Appalachian range formed about the same time that life was first colonising land, ~480 mya, and it's likely that soil formation post-dates this by a significant extent.
This also means that the Appalachians have some of the oldest rivers in the world, including the ... inaccurately named ... New River, the Susquehanna, and French Broad River, all dating to ~260--340 mya.
In the case of the New River (unsure about the others), it is the other way around: the river is not old because the mountains are old, but the mountains are old because the river is older. The New River predates the mountains that surround it.
That said, the river runs through the Appalachians, and is quite old.
Older than bones, older than bones.
On the other hand if we could convince them to get back together the shipping costs to Europe would plummet and that would be good for the economy.
Edit: My mistake, thought you were referring to the original “older than trees” comment.
The higher and more rugged the range, the younger, in all likelihood.