Really? Astronomers cannot pinpoint the exact dates of occurrences of the Vela or Geminga supernovas. How can you statistically filter out fluctuations in carbon-14, if you don't know when to begin? The crab nebula formed from a supernova that Chinese astronomers recorded in 1054 A.D. A spike from that supernova could be reliably filtered out; spikes from supernovas that are 2-5 times older than the half-life of carbon-14 itself would be difficult to isolate and correct for.
There is a natural C-14 level. Supernovas cause temporary spikes in C-14, making things appear older than they are to geologists. Lets say a supernova hit 10000 years ago... this means that we will find nothing that is dated to be 10000 years old, but we will find more stuff dated at 10000+x years old due to the supernova spike. That's how.
Interestingly, the Vela supernova exploded 13,000 years ago, before God created the universe...

Which brings up another problem: why is it that some Precambrian graphite samples have carbon 14 ages of about 60,000 years? Shouldn't such fossils be "carbon-14 dead"?
From wiki:
"Sensitivity has since been greatly increased by the use of accelerator-based mass-spectrometric (AMS) techniques, where all the 14C atoms can be counted directly, rather than only those decaying during the counting interval allotted for each analysis. The AMS technique allows one to date samples containing only a few milligrams of carbon, although the maximum age reported is still around 60,000 years."