A textbook, describing a qualitative test for the $\ce{Al^3+}$ cation in which you use $\ce{NH4Cl}$ and $\ce{NH4OH}$ to precipitate $\ce{Al(OH)3}$, mentioned that the solubility of this precipitate decreases in the presence of the ammonium salt.
I sort of reasoned it out to the common-ion effect decreasing the $\ce{OH-}$ concentration before I wondered why that would have an effect at all. As far as I know, the solubility of a salt only varies with the solvent used, the pressure, and the temperature (and of course, on the common-ion effect if it's present).
I made up an explanation, that a more dissociated solvent wouldn't have to physically contort to solvate the salt ions; that when the bonds are broken, the ions of the solvent can more freely arrange themselves in optimal positions to stabilize the salt constituents.
Is that line of reasoning correct? If not, how can the relation between solvent dissociation and salt solubility be rationalized?