  The prompt emission spectra of gamma-ray bursts (GRBs) usually have a
dominant component that is well described by a phenomenological "Band"
function. The physical origin of this spectral component is debated. Although
the traditional interpretation is synchrotron radiation of non-thermal
electrons accelerated in internal shocks or magnetic dissipation regions, a
growing trend in the community is to interpret this component as modified
thermal emission from a dissipative photosphere of a GRB fireball. We analyze
the time dependent spectrum of GRB 110721A detected by {\em Fermi} GBM and LAT,
and pay special attention to the rapid evolution of the peak energy $E_p$. We
define a "death line" of thermally-dominated dissipative photospheric emission
in the $E_p - L$ plane, and show that $E_p$ of GRB 110721A at the earliest
epoch has a very high $E_p \sim 15$ MeV that is beyond the "death line".
Together with the finding that an additional "shoulder" component exists in
this burst that is consistent with a photospheric origin, we suggest that at
least for some bursts, the "Band" component is not from a dissipative
photosphere, but must invoke a non-thermal origin (e.g. synchrotron or inverse
Compton) in the optically thin region of a GRB outflow. We also suggest that
the rapid "hard-to-soft" spectral evolution is consistent with the quick
discharge of magnetic energy in a magnetically-dominated outflow in the
optically thin region.
