Some corals can be carbon dated, and also dated by another radioactive material, Thorium-230.Pollen found in the Greenland icecap has been carbon dated, and also dated by counting ice layers. Trees grow a thick ring in a good year, and grow a thin ring in a bad year.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.
However, even this small an adjustment was a bit of a shock.
It is also standard to coat fossils during their extraction and transport.
Acetone is sometimes used while extracting fossils, because it dissolves dirt.
Then, we have wood for which we know the right answer.
So, carbon dating has been calibrated against the rings of California bristlecone pines, and Irish bog oaks, and the like.
For example, Stonehenge suddenly became older than the Pyramids, instead of younger.