Interesting question, Ned. What do we mean by "correlation"? I guess I'm thinking in terms of 18th century (pre-Darwin!) geology (practiced by Christians!). Certain fossils always occurred in the same order in the stratigraphic record, no matter which country you were looking at. It came to be realized that what they were seeing is that very distinctive life existed at different epochs in earth's history. It was then hypothesized that if you saw the same fossils in two strata in two widely separated places, those strata were laid down at the same time. (This hypothesis was confirmed, of course, by radiometric dating.)
To answer a very much earlier question, Ned, I would say that since organic bone is a very different material than a mineralized fossil, it should be easy to tell whether a fossil was eroded out of the original material and transported after fossilization. But, then, I am not a geologist.