To any scientist that does any lab work, this isn’t true even on the face of it. There is always analytic error and sources of methodological error.
Let’s look at this problem carefully. For there to be no C14 we have to first assume that no nitrogen atoms in the sample were converted to 14C by surrounding radiation. Afterall, this is the process that creates 14C in our upper atmosphere. Any nitrogen in the sample could also be converted through this process.
Second, we have to rule out the possibility that environmental carbon is introduced into the sample after collection and during carbonization. Obviously, there are many steps where this can occur, including chemical reactions that will covalently attach atmospheric carbon dioxide to the sample. The method of extracting carbon from the sample will also introduce trace amounts of modern carbon. There is also contamination of the fossil with carbon found in the ground itself, such as percolating water.
Third, we have the instrument itself. Carbon from past samples and environmental contamination can be present in the chamber being used for detection.
There is absolutely no expectation that a fossil billions of years old will have zero 14C. There is every reason to believe that a sample from a billions of years old fossil will have detectable amounts of 14C.