  Classical Wolf-Rayet (WR) stars are massive, hydrogen depleted, post
main-sequence stars that exhibit emission-line dominated spectra. For a given
metallicity Z, stars exceeding a certain initial mass M_single(Z) can reach the
WR phase through intrinsic mass-loss (single-star channel). Stars of lower
masses can reach the WR phase via binary mass transfer (binary channel). It is
commonly assumed that the binary channel dominates the formation of WR stars in
environments with low Z such as the SMC and LMC. However, their reported WR
binary fractions of 30-40% are comparable to that of the Galaxy. Here, we
explain this apparent contradiction by considering the minimum initial mass
M_spec(Z) needed for the stripped product to appear as a WR star. We calibrate
M_spec(Z) using the lowest-luminosity WR stars in the Clouds and the Galaxy. A
range of M_single(Z) values are explored using various evolution codes. We
estimate the additional contribution of the binary channel by considering the
interval [M_spec(Z), M_single(Z)], which characterises the initial-mass range
in which binaries can form additional WR stars.
  Results: The WR-phenomenon ceases below luminosities of logL = 4.9, 5.25, and
5.6 [Lsun] in the Galaxy, LMC, and SMC, which translates to He-star masses of
7.5, 11, 17 Msun and initial masses of M_spec = 18, 23, 37 Msun. Stripped stars
with lower initial masses in the respective galaxies would tend to not appear
as WR stars. M_single lies in the range 20-30, 30-60, and > 40 Msun for the
Galaxy, LMC, and SMC. We find that that the additional contribution of the
binary channel is a non-trivial function of Z that cannot be conclusively
claimed to be monotonically increasing with decreasing Z. Hence, one should not
a-priori expect that binary interactions become increasingly important in
forming WR stars at low Z, or that the WR binary fraction grows with decreasing
Z.
