The only microlensing events toward the Magellanic Clouds for which the loc
ation of the lens is strongly constrained are the two binary caustic crossi
ng events. In at least one and possibly both cases, the lens lies at or clo
se to the Magellanic Clouds themselves. On the face of it, this seems an im
probable occurrence if the Galactic dark halo provides the bulk of the lens
ing population, as suggested by standard analyses of the MACHO data set tow
ard the Large Magellanic Cloud (LMC). We use a binomial statistic to assess
the prior probability of observing M nonhalo binary caustic events given a
total sample of N caustic binaries. We generalize for the case of multicom
ponent Galactic and Magellanic Cloud models the Bayesian likelihood method
for determining the lens mass and halo fraction from the observed timescale
s. We introduce a new statistic, the "outcome discriminator," which measure
s the consistency between the binary caustic data, prior expectation, and t
he MACHO two-year LMC data set as a whole. If the Magellanic Clouds are not
embedded in their own dark halos of MACHOs, then the discovery of two nonh
alo caustic binary events out of two (M = N = 2) is inconsistent with expec
tation given the MACHO data set. Galactic models in which M = 1 is the like
liest outcome are also inconsistent with the data, although models in which
M = 1 has a reasonable prior probability are not. We consider the possibil
ities that the Magellanic Clouds are embedded in dark haloes of their own o
r that the Galactic halo is intrinsically deficient in the binary systems t
hat produce caustic crossing events. Either of these possibilities provide
greater compatibility between observation and prior expectation, although t
he idea of Magellanic haloes is perhaps the more natural of the two and has
support from kinematical studies.