If this water is in contact with significant quantities of limestone, it will contain many carbon atoms from dissolved limestone.
Since limestone contains very little, if any, radiocarbon, clam shells will contain less radiocarbon then would have been the case if they had gotten their carbon atoms from the air.
There is, in fact, no indication anywhere in the original reference that these samples were from the "Pennyslvanian"; nor is there any hint that they were expected to be "300 million years old"; these appear to be purely apocryphal embellishments to the original account.
Surely, what the Russians intended to convey (and what nearly everybody would understand), is that these samples were charcoal from a not too ancient campfire.
This gives the clam shell an artificially old radiocarbon age.
This problem, known as the "reservoir effect", is not of very great practical importance for radiocarbon dating since most of the artifacts which are useful for radiocarbon dating purposes and are of interest to archaeology derive from terrestrial organisms which ultimately obtain their carbon atoms from the air, not the water.
Such stories misrepresent the truth and do a disservice to science and public knowlege.
A common misconception about radiocarbon dating is that it gives a precise date---3577 B. In actual practice radiocarbon dating can only give a range of dates for a given sample---3650 to 3410 B.
C., for example---the true date lying somewhere in that range.
(Aardsma, 1994, page 2.)The original reference [Trautman and Willis, page 200.] in the second case (natural gas) immediately reveals that both Whitelaw and The Answers Book have, unfortunately, neglected several very important " The sensitivity of the equipment used to make the radiocarbon measurements on these natural gas samples was limited to 30,000 to 34,000 years---the equipment was unable to measure back further. In this example, old radiocarbon dates from living clams or snails are given as evidence which discredits the reliability of radiocarbon dating. Aardsma addressed this issue in a 1989 article: The shells of freshwater clams can, and often do, give anomalous radiocarbon results.
However, the reason for this is understood and the problem is restricted to only a few special cases, of which freshwater clams are the best-known example.