Historians don't have "right answers" for really old things.
However, carbon dating has done well on young material like the Dead Sea Scrolls, the Minoan ruins, and acacia wood from the tomb of the pharoah Zoser.
It is also standard to coat fossils during their extraction and transport.
Acetone is sometimes used while extracting fossils, because it dissolves dirt.
In short, unless you have evidence to the contrary, you should assume that most of the carbon in a fossil is from contamination, and is not originally part of the fossil. The nuclear tests of the 1950's created a lot of C14.
Also, humans are now burning large amounts of "fossil fuel".
Then, we have wood for which we know the right answer.