I'm making the measurements with Agilent's 34410A 6.5 digit multimeter (last calibrated in June 2013)...through a 1k resistor! Oops. Looks like I forgot to take into account the current draw of my multimeter. You are right. If I take the measurement at the DAC's output pin then everything looks fine.
One more question please. The datasheet states that output current is clamped at the maximum value (8mA). Does that mean that short-circuiting the analog outputs is within spec and will not cause any damage to the DAC? I would like to avoid using any active buffering on the outputs.