For a amp used in BGR, that deals with only diode voltages, the ICMR need to only include 0.5 to 0.8., assuming that there is no latch-up when these limits are breached.
Working CMR of 0.5 to 0.8 is enough assuming that there is no catastrophe outside it. Eventhough your circuit may not need to function there, these ranges will be exercised during start-up, power-up transients. Common-mode induced latch-up is an old phenomenon that causes output phase reversal when ICMR exceeds limits. I included it just for generality. In your CMOS circuit you don't have to worry about it.
I think he means as long as your amplifier is functioning with inputs ranging from 0.5v ~ 0.8v, your circuit should be fine. Your ICMR MAX can be as high as you want but no lower than 0.8V. 0.5v~0.8v comes from VBE of the BJT I think.