We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) appears as fluctuations of the quenched density of a 1D random walk whose transition probabilities are iid $[0,1]$-valued random variables. A naive chaos expansion fails for this model. Instead we use the fact that in this regime, the quenched density solves a discrete SPDE which resembles the SHE. We furthermore show that independent noise is generated in the limit. This is joint work with Sayan Das and Hindy Drillick.