  We calculate X-ray signal that should arise due to reflection of the putative
collimated X-ray emission of the Galactic supercritical accretor SS 433 on
molecular clouds in its vicinity. The molecular gas distribution in the region
of interest has been constructed based on the data of the BU-FCRAO GRS in
$^{13}$CO $J=1\rightarrow0$ emission line, while the collimated emission was
assumed to be aligned with the direction of the relativistic jets, which are
continuously launched by the system. We consider all the available $Chandra$
observations covering the regions possibly containing the reflection signal and
put constraints on the apparent face-on luminosity of SS 433 above 4 keV. No
signatures of the predicted signal have been found in the analysed regions down
to a 4-8 keV surface brightness level of $\sim 10^{-11}$ erg/s/cm$^2$/deg$^2$.
This translates into the limit on the apparent face-on 2-10 keV luminosity of
SS 433 $L_{X,2-10}\lesssim 8\times10^{38}$ erg/s, provided that the considered
clouds do fall inside the illumination cone of the collimated emission. This,
however, might not be the case due to persisting uncertainty in the
line-of-sight distances to SS 433 $d_{SS433}$ (4.5-5.5 kpc) and to the
considered molecular clouds. For half-opening angle of the collimation cone
larger than or comparable to the amplitude of the jets' precession
($\approx21\deg$), the stringent upper limit quoted above is most relevant if
$d_{SS433}<5$ kpc, provided that the kinematic distances to the considered
molecular clouds are sufficiently accurate. Dropping the last assumption, a
more conservative constraint is $L_{X,2-10}\lesssim10^{40}$ erg/s for
$d_{SS433}=4.65-4.85$ kpc (and yet worse outside this range). We conclude that
SS 433 is not likely to belong to the brightest ultraluminous X-ray sources if
it could be observed face-on, unless its X-ray emission is highly collimated.
(Abridged)
