Oh no, there ARE several others including:
1) the object being tested was not contaminated with more recent, or older carbon.2) the ratio of C14/C12 in the atmosphere has remained constant (which it has not --the observed change in the 20th century is some of the strongest evidence that the rise in CO2 concentration in the atmosphere is anthropogenic, DAGS "Suess effect"). It also varies with variations in cosmic ray flux.
3) That C14 was not preferentially incorporated into the object vs C12, or vice versa.Those are only assumptions until they are tested. If validated, they become conclusions. In some cases other studies permit calibrations to compensate for the inaccuracy of the assumption. For instance, measuring the C14/C12 ration in tree rings allows a calibration to compensate for '2', above.