I noticed the common mode input range on the analog inputs is rather unusual on the minimum end. I assume by "Vin" they mean Vref/PGA.
Inserting this into the common mode range formula gives us a common mode minimum of AVSS + 0.1 + (Vref/2). If I used a unipolar analog supply and the internal Vref 2.048 V, this means the common mode minimum is a rather restrictive 1.124V which will make the part a little unfriendly towards ground referenced single ended measurements. I did try applying 0.5V and 0V differentially to the analog inputs (i.e. 0.5V single ended), which would be well outside this minimum common mode range, and the digitized result was correct. Either I am interpreting the minimum common mode formula incorrectly or TI has built a fair amount of margin into this measurement. Can you verify I have interpreted the minimum common mode limit formula correctly?