We demonstrate analytically a novel scheme to obtain polarization-independent operation in low-cost coherent OOK receivers, suitable for access networks. We move from a well-known phase-diversity receiver, exploiting a 3$,times,$3 coupler, three photodiodes, and basic analogue processing. If that receiver is modified to inject the local oscillator (or the signal) into two inputs with proper polarization states, we show, by both mathematical derivation and numerical simulations, that the resulting electrical signal can be polarization-independent; this is attained only if the frequency-detuning between the signal carrier and the local oscillator is high enough, so that intrinsic second order distortions can be spectrally isolated and suppressed by the low-pass filtering of the receiver.