when the input signal exceeds the supply voltage, but it does. How can that be?
It is important to distinguish between over-voltage protection (i.e. the
ability of an IC to withstand input voltages greater than the power supply
voltage) and output phase reversal (a part specific phenomenon, where the
output is inverted as the input common mode approaches or exceeds the supplies).
The AD822 is not damaged when the input voltage exceeds 0.2V provided the input
current is limited to less than 10mA. However, the output may go into phase
reversal when the input exceeds the supplies.
In any case, the absolute maximum ratings supercede anything else in the
datasheet and should be respected at all times.
Consider the AD8512, AD8572, AD8552 as alternative rail to rail output, FET
input, single supply opamps.