  The presence of quasars at redshifts z > 6 indicates the existence of
supermassive black holes (SMBHs) as massive as a few times 10^9 Msun,
challenging models for SMBH formation. One pathway is through the direct
collapse of gas in T_{vir} > 10^4 K halos; however, this requires the
suppression of H_2 cooling to prevent fragmentation. In this paper, we examine
a proposed new mechanism for this suppression which relies on cold-mode
accretion flows leading to shocks at high densities (n > 10^4 cm^{-3}) and
temperatures (T > 10^4 K). In such gas, H_2 is efficiently collisionally
dissociated. We use high-resolution numerical simulations to test this idea,
demonstrating that such halos typically have lower temperature progenitors, in
which cooling is efficient. Those halos do show filamentary flows; however, the
gas shocks at or near the virial radius (at low densities), thus preventing the
proposed collisional mechanism from operating. We do find that, if we
artificially suppress H_2 formation with a high UV background, so as to allow
gas in the halo center to enter the high-temperature, high-density "zone of no
return", it will remain there even if the UV flux is turned off, collapsing to
high density at high temperature. Due to computational limitations, we
simulated only three halos. However, we demonstrate, using Monte Carlo
calculations of 10^6 halo merger histories, that a few rare halos could
assemble rapidly enough to avoid efficient H_2 cooling in all of their
progenitor halos, provided that the UV background exceeds J_{21} ~ few at
redshifts as high as z ~ 20.
