  The timing properties of X-ray binaries are still not understood,
particularly the presence of quasi-periodic oscillations (QPOs) in their X-ray
power spectra. The solid-body regime of Lense-Thirring precession is one
prominent model invoked to explain the most common type of QPOs, Type C.
However, solid-body precession requires a specific structure that has not been
examined in light of constrained properties of accretion flows. We assume in
this paper, as solid-body precession requires, a disk separated into two flows
at a transition radius $r_t$: a cold outer flow and a hot inner flow (playing
the role of the corona). We explore the physical structure of both flows using
model-independent estimates of accretion parameters. We show that, in order to
reproduce the observed X-ray spectra during luminous hard states, the hot flow
must accrete at sonic to supersonic speeds, unreachable with typical viscous
torques. As a result of this extreme accretion speed (or high $\alpha$
parameter), no region of the disk during these states lies in the `wave-like'
regime required for solid-body precession. Furthermore, we expect the flow to
align with the black hole spin axis via the Bardeen-Petterson effect inside a
radius $r_{\rm break}>r_t$. As a consequence, the hot inner flow cannot exhibit
solid body precession -- as currently pictured in the literature -- during
luminous hard states. Since Type C QPOs are prevalent in these states, we
conclude that this mechanism is unlikely to be responsible for producing Type C
QPOs around stellar mass black holes.
