I like the role reversal, so why not give it a try.
There are radioactive elements naturally occuring on the Earth today that have relatively short half lives (C-14 5,000 years I believe). Scientists claim that these elements are being constantly produced, e.g. C-14 is produced in the uppper atmosphere/ionosphere. However, it cannot be argued with any certainty that every radioactive atom with a short half life has been produced by these means. Therefore, without certainty, C-14 could be proof of a YE.