Having the output of a power supply isolated means it has no galvanic connection to the power line. However, for safety reasons the frame/chassis of the supply should be grounded to the power line grounding circuit. The output remains isolated.
One reason for connecting the chassis to the utility ground is to avoid random drifting of the chassis to almost any voltage, which can cause some surprises, tantamount to walking across a carpet on a dry wintry day and touching a doorknob.
The user of the equipment has the option of connecting either polarity of the output to ground or anything else, or not connecting it at all.