How can we know how old fossils are?

[Anomalocaris]

Intriguingly, that does not appear to always be true.

Intriguingly, it is always and absolutely true.  There is no organic material in fossils.  Fossils are organic materials that have been replaced by minerals.  Very rarely, organic material is found encased within fossils or near fossils or on fossils, but not in the fossils themselves.

And that, my friend, is how you split hairs. 

Boru

Well, sir, the hair remains unsplit

You see, in the tyrannosaurs femur in question, the unmineralized, original soft tissue material is completely enclosed inside mineralized fossil bone.    Thus there is organic material in the fossil, in much the same way as there is candy in the box.

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I've never heard of carbon being referred to as "tissue".

What is in the tyrannosaur femur is much more than just carbon.   The material is soft and elastic, and form branching tubular structure inside the vascular parts of the bone just like the blood vessels, and even have remains of blood cells inside.  

The soft tissue remains extracted from tyrannosaur fossil proved sufficiently chemically well preserved, despite destruction of any possible remaining DNA, that proteins remarkably similar to those which are unique to birds were identified in it.  Given the extremely close evolutionary relationship between the tyrannosaurs branch of the dinosaurs lineage and avian birds, this is additional evidence the soft organic material found inside the dinosaur bone fossil is the original tissue from the dinosaur, and not some later organic contaminant that somehow got inside the fossilized bone.