In this Letter we propose a new view on the phenomenon of Algol-type minima in the light curves of UX Orionis stars (UXORs). The idea is based on the earlier proposal by various authors that UXORs are nearly edge-on disks in which hydrodynamic fluctuations could cause clumps of dust and gas to cross the line of sight. However, early models of protoplanetary disks were based on the notion that these have a flaring geometry. If so, then it is mostly the outer regions of the disk that obscure the star. The timescales for such obscuration events would be too long to match the observed timescales of weeks to months. Recent two-dimensional self-consistent models of Herbig Ae/Be protoplanetary disks, however, have indicated that for Herbig Ae/Be star disks there exists, in addition to the usual flared disks, a new class of disks: disks that are fully self-shadowed. For these disks only their puffed-up inner rim (at the dust evaporation radius) is directly irradiated by the star, while the disk at larger radius resides in the shadow of the rim. For these disks there exist inclinations at which the line of sight toward the star skims the upper parts of the puffed-up inner rim, while passing high over the surface of outer-disk regions. These outer-disk regions therefore do not obscure the star nor the inner-disk regions, and small hydrodynamic fluctuations in the puffed-up inner rim could cause the extinction events seen in UXORs. If this idea is correct, it makes a prediction for the shape of the SEDs of these stars. It was shown by Dullemond and Dullemond, Dominik, & Natta that flared disks have a strong far-IR excess and can be classified as "Group I" (in the classification of Meeus et al.), while self-shadowed disks have a relatively weak far-IR excess and are classified as "Group II." Our model therefore predicts that UXORs belong to the "Group II" sources. We show that this correlation is indeed found within a sample of 86 Herbig Ae/Be stars.