You show me the bird and I'll show you the positive PCR result.
They need to form their own union.
If there is no influenza RNA present, it is physically impossible to detect it with PCR.
Think of PCR as being similar to photocopying. If you put a sheet of paper on a (clean) copier, will you get an image if you copy it enough times? No. The only way you can get an image in the copies is if the image is on the original paper.
The only way I have ever detected something in PCR is if the thing was present in the original sample. And, due to how PCR works, sometimes the thing cannot be detected even if you know for a fact that it is present in the sample. So, you are more likely to get a negative result from a positive sample than a positive result from a negative sample.
I will point out that it is possible for cross-contaminations to cause false positives. We take measures against that, by cleaning our equipment, using special filtered pipettes, doing the work in a dedicated clean space, etc. But--if a negative sample comes up as a false positive, it means that the nucleic acid you are trying to detect *is* in the area, because it got into the reaction somehow. You can always run the samples again if you have doubts about the outcome.
I've run thousands (tens of thousands?) of PCR reactions. This is something I know quite well.