Abstract: This paper develops a receiver-specific mean-squared-error (MSE) framework for cooperative integrated sensing and communication (ISAC) localization using random orthogonal frequency-division multiplexing (OFDM) payloads. It captures local peak perturbations and incorrect ambiguity-peak acquisition for two classical receiver processing schemes: matched filtering (MF) and reciprocal filtering (RF). For scatterers well separated in delay, we quantify how frequency spread and interference induced by symbol-energy fluctuations affect local delay errors under MF. RF removes symbol-dependent weighting but amplifies noise for low-energy symbols. Payload-conditioned joint Gaussian delay profiles yield peak-selection probabilities, which combine with nonlinear multistatic fusion errors to approximate position MSE while accounting for network geometry. Numerical results illustrate receiver-dependent estimation errors and the benefits of frequency-dependent constellation allocation.