  We report low temperature specific heat and muon spin relaxation/rotation
($\mu$SR) measurements on both polycrystalline and single crystal samples of
the pyrochlore magnet Yb$_2$Ti$_2$O$_7$. This system is believed to possess a
spin Hamiltonian supporting a Quantum Spin Ice (QSI) ground state and to
display sample variation in its low temperature heat capacity. Our two samples
exhibit extremes of this sample variation, yet our $\mu$SR measurements
indicate a similar disordered low temperature state down to 16 mK in both. We
report little temperature dependence to the spin relaxation and no evidence for
ferromagnetic order, in contrast to recent reports by Chang \emph{et al.} (Nat.
Comm. {\bf 3}, 992 (2012)). Transverse field (TF) $\mu$SR measurements show
changes in the temperature dependence of the muon Knight shift which coincide
with heat capacity anomalies. We are therefore led to propose that
Yb$_2$Ti$_2$O$_7$ enters a hidden order ground state below $T_c\sim265$ mK
where the nature of the ordered state is unknown but distinct from simple long
range order.
