  The long standing problem of identifying the emission mechanism operating in
gamma-ray bursts (GRBs) has produced a myriad of possible models that have the
potential of explaining the observations. Generally, the empirical Band
function is fit to the observed gamma-ray data and the fit parameters are used
to infer which radiative mechanisms are at work in GRB outflows. In particular,
the distribution of the Band function's low-energy power law index, $\alpha$,
has led to the so-called synchrotron "line-of-death" (LOD) which is a statement
that the distribution cannot be explained by the simplest of synchrotron models
alone. As an alternatively fitting model, a combination of a blackbody in
addition to the Band function is used, which in many cases provide a better or
equally good fit. It has been suggested that such fits would be able to
alleviate the LOD problem for synchrotron emission in GRBs. However, these
conclusions rely on the Band function's ability to fit a synchrotron spectrum
within the observed energy band. In order to investigate if this is the case,
we simulate synchrotron and synchrotron+blackbody spectra and fold them through
the instrumental response of the $Fermi$ Gamma-ray Burst Monitor (GBM). We then
perform a standard data analysis by fitting the simulated data with both Band
and Band+blackbody models. We find two important results: the synchrotron LOD
is actually more severe than the original predictions: $\alpha_{\bf LOD} \sim
-0.8$. Moreover, we find that intrinsic synchrotron+blackbody emission is
insufficient to account for the entire observed $\alpha$ distribution. This
implies that some other emission mechanism(s) are required to explain a large
fraction of observed GRBs.
