  We identify stars in the $\delta$ Sct instability strip that do not pulsate
in p modes at the 50-$\mu$mag limit, using Kepler data. Spectral classification
and abundance analyses from high-resolution spectroscopy allow us to identify
chemically peculiar stars, in which the absence of pulsations is not
surprising. The remaining stars are chemically normal, yet they are not
$\delta$ Sct stars. Their lack of observed p modes cannot be explained through
any known mechanism. However, they are mostly distributed around the edges of
the $\delta$ Sct instability strip, which allows for the possibility that they
actually lie outside the strip once the uncertainties are taken into account.
We investigated the possibility that the non-pulsators inside the instability
strip could be unresolved binary systems, having components that both lie
outside the instability strip. If misinterpreted as single stars, we found that
such binaries could generate temperature discrepancies of $\sim$300 K -- larger
than the spectroscopic uncertainties, and fully consistent with the
observations. After these considerations, there remains one chemically normal
non-pulsator that lies in the middle of the instability strip. This star is a
challenge to pulsation theory. However, its existence as the only known star of
its kind indicates that such stars are rare. We conclude that the $\delta$ Sct
instability strip is pure, unless pulsation is shut down by diffusion or
another mechanism, which could be interaction with a binary companion.
