Why would a power supply unit with insulating case and galvanic separation need a grounded power cord?
Below is a typical schematic of an AC/DC power supply EMI filter.



You can see that the X-capacitors (between line and neutral) plus the leakage inductance of the common-mode inductor give the differential-noise rejection, and the CM choke inductance combined with the Y-capacitors give the common-mode noise rejection.

I would also not be surprised if the output return  is directly connected to earth.