Stochastic fluctuations in signaling and gene expression limit the ability of cells to sense the state of their environment, transfer this information along cellular pathways, and respond to it with high precision. Mutual information is now often used to quantify the fidelity with which information is transmitted along a cellular pathway. Mutual information calculations from experimental data have mostly generated low values, suggesting that cells might have relatively low signal transmission fidelity. In this work, we demonstrate that mutual information calculations might be artificially lowered by cell-to-cell variability in both initial conditions and slowly fluctuating global factors across the population. We carry out our analysis computationally using a simple signaling pathway and demonstrate that in the presence of slow global fluctuations, every cell might have its own high information transmission capacity but that population averaging underestimates this value. We also construct a simple synthetic transcriptional network and demonstrate using experimental measurements coupled to computational modeling that its operation is dominated by slow global variability, and hence that its mutual information is underestimated by a population averaged calculation.