Carbon dating can not be used for fossils (except maybe for very recent fossils). Therefore fossils can normally only be dated from their strata. But of course the strata itself is not dated from the fossil data - this would not make any logical sense because you don't have a fossil data without dating the strata first.

Strata can be dated in several ways, like from its depth, its magnetic orientation (the history of the magnetic field is well known), or from vulcanic stones in that strata, using the 235U -> 207Pb decay. Combining several dating methods normally gives a pretty accurate date of that strata. There are not several tests tried until one fits - all suitable tests must fit or the whole measurement is scientifically worthless.