This is a strong case to use RSSI to reject bad signals.  

Your assumptions include that all noise is detected as random data, which does not appear to be true in your case.  Analysis requires details of the design to see what data patterns are detected with statistical analysis.  Perhaps Bias, asymmetry and filtered noise from LO leakage and stray noise are causing pattern bias from ambient signals.  CRC length will help as expected only if noise is detected as pure random.

Another such example of non-random patterns is Rician Fading of stray transmitters in-channel modulates distortion according to reflection path interference length.