Diff. Amplifier with Single Supply Opamp - Strange Behavior
The act of setting OUTA high lifts the inverting input of the diff amp high and forces a current into OUTB output. This will produce an offset error on OUTB's output.

If you look on page 6 of the DS it shows this effect (output swing capability) but it doesn't really indicate how poor this will be with a 200 kohm. It can be seen at 1 kohm (about 0.1 volt offset induced).

Given also that to produce close to 0 volts on an output when the device itself receives no power rail below 0 volts is a tall ask and it will be susceptible to pull-up effects.

Please also ensure you measure the output relative to the common 0 volt pin on the device.

As a general rule I never rely on the top or bottom 20 mV range on dacs or adcs.