Using an alternative scheme to generate correlated noise, we have reexamined issues of stochastic growth and directed polymer wandering subject to spatially correlated disorder. Our findings explicitly confirm relevant exponent equalities associated with the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)], thereby establishing important universal aspects. In addition, we show that the basin of attraction of the short-ranged fixed point function certainly extends to correlations falling inversely with separation, as previously conjectured.