The shells of live 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.
There are two characteristics of the instrumental measurement of radiocarbon which, if the lay observer is unaware, could easily lead to such an idea.
For example, a sample with a true radiocarbon age of 100,000 radiocarbon years will yield a measured radiocarbon age of about 20,000 radiocarbon years if the sample is contaminated with a weight of modern carbon of just 5% of the weight of the sample's carbon.
It is not too difficult to supply contaminating radiocarbon since it is present in relatively high concentrations in the air and in the tissues of all living things including any individuals handling the sample.
By radiocarbon dating a piece of wood which has been dated by counting the annual growth rings of trees back to when that piece of wood grew, a calibration table can be constructed to convert radiocarbon years to true calendar years.
Of course, the table, so constructed, will only give the correct calibration if the tree-ring chronology which was used to construct it had placed each ring in the true calendar year in which it grew.
I am not aware of any authentic research which supports this claim.