That is (errr, was) conventional wisdom. However, a recent paper by James and Markowski looked at the effects of dry air aloft on deep convection, and their results are contrary to what most of us had thought about when it comes to mid-level moisture and evaporational cooling. In their supercell case, the drier mid-level air initially caused greater evaporation of hydrometeors, but this reduced precipitation/water loading [precip loading imparts negative buoyancy that can reduce updraft intensity / increase downdraft intensity]. The reduced water loading makes up for (+/-) evaporational cooling in their simulations.
See: James and Markowski, 2010:
A numerical investigation of the effects of dry air aloft on deep donvection
I'll take the following snippet from the abstract:
"A three-dimensional cloud model was used to investigate the sensitivity of deep convective storms to dry air above the cloud base. In simulations of both quasi-linear convective systems and supercells, dry air aloft was found to reduce the intensity of the convection, as measured by updraft mass flux and total condensation and rainfall. In high-CAPE line-type simulations, the downdraft mass flux and cold pool strength were enhanced at the rear of the trailing stratiform region in a drier environment. However, the downdraft and cold pool strengths were unchanged in the convective region, and were also unchanged or reduced in simulations of supercells and of line-type systems at lower CAPE. This result contrasts with previous interpretations of the role of dry air aloft in the development of severe low-level outflow winds....
When dry air was present, the decline in hydrometeor mass exerted a negative tendency on the diabatic cooling rates and acted to offset the favorable effects of dry air for cooling by evaporation.
Thus, with the exception of the rearward portions of the high-CAPE line-type simulations, dry air was unable to strengthen the downdrafts and cold pool. A review of the literature demonstrates that observational evidence does not unambiguously support the concept that dry air aloft favors downdraft and outflow strength. It is also shown that the use of warm rain microphysics in previous modeling studies may have reinforced the tendency to overemphasize the role of dry air aloft."
(emphasis added by me)