Power-law scaling in coarse-grained data has been linked to critical dynamics, but the true source of this scaling often remains unclear. Here, we analyze neural activity recorded during spatial navigation, reproducing power-law scaling under a phenomenological renormalization group (PRG) procedure that clusters units by activity similarity. Such scaling was previously characterized as describing a non-trivial fixed point. We show that the iterative nature of the procedure itself leads to the emergence of power laws when applied to a non-critical model consisting of heterogeneous, non-interacting units obeying spatially structured activity. Furthermore, the scaling exponents produced by heterogeneous non-interacting units match the observed exponents in recorded neural data. A simplified version of the PRG further reveals how heterogeneity smooths transitions across scales in our model, mimicking critical behavior. The resulting exponents depend systematically on system and population size, predictions confirmed by subsampling the data, further distinguishing these effective PRG exponents from true critical exponents.