  We follow the inspiral and merger of equal-mass black holes (BHs) by the
moving puncture technique and demonstrate that both the exterior solution and
the asymptotic gravitational waveforms are unchanged when the initial interior
solution is replaced by constraint-violating ``junk'' initial data. We apply
this result to evolve conformal thin-sandwich (CTS) binary BH initial data by
filling their excised interiors with arbitrary, but smooth, initial data and
evolving with standard puncture gauge choices. The waveforms generated for both
puncture and filled-CTS initial data are remarkably similar, and there are only
minor differences between irrotational and corotational CTS BH binaries. Even
the interior solutions appear to evolve to the same constraint-satisfying
solution at late times, independent of the initial data.
