What would the output of this ADC be?
It no longer makes sense to say Vref = 2V in a bipolar single-ended ADC.  You now have Vref-, which is converted as full-scale low, and Vref+, which is converted to full-scale high.  Inputs between your two reference inputs will be linear (within the linearity error), and inputs beyond either of the references will either be clipped or destroy the device (depending on whether you respect the maximum ratings).  This is sometimes called pseudo-differential, because it is the same as subtracting the negative reference from all other analog inputs.

However, the ADS1282 would be better described as fully differential.  In this case the inputs are not limited to the range determined by the references; a common-mode signal may exist which will be cancelled as long as the input range determined by the power supplies is not exceeded.  And it does not make any sense to talk about an input of +1V, or -1V.  You have two inputs per channel, and the difference and common-mode offset are both important.

In the context of the power supply, an ADC supporting bipolar supplies simply means that AVSS is not tied to DVSS.