We suggest that the near-infrared emission of many Herbig Ae/Be stars arises in surrounding dusty envelopes, rather than circumstellar disks. Hillenbrand et al. and Lada & Adams showed that circumstellar disk models which reproduce the approximately 3 mum peaks in the near-infrared spectral energy distributions of Ae/Be stars must have high accretion rates, and must either be transparent in their inner regions, or have physical inner disk ''holes.'' However, we show that disks around Ae/Be stars are likely to remain optically thick at the required accretion rates. Alternatively, the assumption of a physical hole in the disk implies either that large amounts of material pile up at approximately 10 stellar radii or that approximately 90% of the accretion luminosity escapes detection. To avoid these difficulties we propose that the infrared excesses of many Ae/Be stars originate in surrounding dust nebulae instead of circumstellar disks. These dust envelopes could be associated with the primary star or a nearby companion star. One picture supposes that the near-infrared emission of the envelope is enhanced by the same processes that produce anomalously strong continuum emission at temperatures approximately 1000 K in reflection nebulae surrounding hot stars. This near-infrared emission could be due to small grains transiently heated by ultraviolet photons. Some Ae/Be stars show evidence for the 3.3-3.6 mum emission features seen in reflection nebulae around hot stars, which lends further support to this suggestion. Given the difficulties of applying circumstellar disk models to Ae/Be stars, dusty nebula hypotheses deserve further consideration.