The point is that once you change to the internal referance only voltages below that will be measured, so you have to use a potential divider to do that. Say you have a five to one divider, then exactly five volts on the power will give you one volt you can measure. As the five volt supply changes then so will your reading, because the referance is fixed.
Does this mean I can count on the internal reference voltage not to change even if my Arduino's 5V rail were indeed unstable?
but I don't know whether the dips and spikes I'm getting are too brief to register on the multimeter.
The sensor I'm using is powered by the Arduino's 5V supply. What's the reason for dropping the voltage and using a 1.1V reference instead of the 5V default?