Well, in this case the authors of the PDF are describing what other researchers did in the face of anomalous results. It is not the current authors that have ruled out mundane explanations. It is the primary researchers that have no explanation. The problem is extremely evident by what the original researchers did to rid themselves of this strange result. They could neither get rid of the anomaly nor could they explain it.
The position the authors take in the face of these conflicts is that this 14C, which should not be present according to their framework, represents ‘contamination’ for which they currently have no explanation.
No, that's the current authors' oversimplified characterization of the work of the primary researchers. Plus, they then go on to admit that primary researchers *do* have a "mundane explanation", and that explanation is contamination. The current authors discount that explanation, but that doesn't magically make it true that the "primary researches have no explanation". So contrary to your assertions, the primary researchers *do* have an explanation, and it *is* the current authors who have chosen to rule it out.
Furthermore, I'm not sure they've even read the work of the primary researchers, since all their data and cites from those works appear to be cribbed directly from Giem's earlier compilation of results.
Additionally, they give a misleading description of Giem's examination of the in situ generation issue. They write, "He [Giem] shows contamination of the C-bearing fossil material in situ is unlikely..." The problem is that Giem *only* examined whether C14 could be generated in situ by N14 to C14 conversion, and (rightly, I believe) decided it wasn't likely to produce enough C14 to account for the amounts found. *However*, he did *not* examine other processes which could generate new C14 in place, including the crucial U/Th decay which is known to produce C14. The authors either didn't notice that Giem did not cover this alternative source, or chose not to disclose it.
"The position the authors take in the face of these conflicts is that this 14C, which should not be present according to their framework, represents ‘contamination’ for which they currently have no explanation."
That refers *only* to citation #30, and describes their inability to explain why C14 levels would be correlated with species. It's not a summation of all the "primary researchers".