Carbon-12 is stable. Carbon-14 is not stable, and has a half life of about 5700 years.
Carbon-14 is generated in the atmosphere by cosmic rays hitting a Nitrogen atom, and the atmospheric concentration of C14 to C12 is about one in a trillion.
Natural atmospheric CO2 can be created with any kind of Carbon atom, but fossil fuels will only create C02 with C-12 atoms (since the C-14 atoms would have long decayed). So if we find out that recently the atmospheric concentration of C(14)02 to C(12)O2 is different than the concentration of atmospheric C-14 to C-12, then we can determine the quantity of CO2 in the atmosphere that is created by burning fossil fuels.
Following along that same line of data, we can also take ice core samples and examine the atmospheric makeup in the past, so that we can verify to check natural levels of C(14)O2, and ensure that they are much lower than current levels.
I am not familiar with Thomas Friedman, but it seems to me like his explanation of the evidence is just a bit dumbed down so that he doesn't have to explain the periodic table, isotopes, stable and unstable atoms, decay rates, and the other sorts of things that average day-to-day people gloss over at. :)