The problem with the term saturation is that it means different things for bipolar and MOS transistors.
For a MOS diffpair the transistors should work in saturation because then they act like voltage controlled current sources. The drain-source voltage has to be higher than the saturation voltage.
For a bipolar diffpair the transistor should operate in forward-active mode, which means that the base-collector diode is reverse biased. The resulting field will remove carriers from the base and the transistor works as an amplifier. If the base-collector diode becomes forward biased the transistor saturates, which is an undesired condition.
Looking at the base-collector diode we see that two things can drive the transistor into saturation. Increasing the base voltage too much or decreasing the collector voltage too much.
If the resistors RC are too big then it is possible that the voltage drop across them is sufficiently high to push the collector voltage low enough to drive the transistor into saturation.
Therefore it is required to pick a proper value for the RCs.