Negative Voltage Ccfl Inverter from AC Adapter
Using batteries to explain relative voltages for various connections is legitimate if the power-supplies have isolated outputs. If, as you fear in this case, the output ground or common is connected to mains earth then this would not be the case. To figure this out we need to study the datasheet.



Figure 1. From page two of the datasheet we can see that input and output grounds are named differently as GND and OUT GND. This is our first sign of hope that the supply is isolated.



Figure 2. Page 3 lists various connection configurations. The naming convention is continued here but there is no additional information.

Based on Figures 1 and 2 it looks likely that GND and OUT GND are isolated. You can confirm this with a (dis)continuity check using your multimeter. If there is no connection then you are free to connect the + output to your circuit common.

Note that even if there is a through connection you could supply the device from an isolated 24 V PSU and there would be no ground reference.

If any of this needs further elaboration then please add a block diagram or schematic in your original post and comment below to let me know. There's a schematic button on the editor toolbar.