Power supplies with medical safety approval
If the supply is designed, tested, and certified to meet the requirements of 60601, then it does not have that problem.  First, the Y capacitors in the power line filter and the output stage have a smaller value, which increases the leakage current impedance and reduces the earth ground current.  Second, look into SELV:

https://en.wikipedia.org/wiki/Extra-low_voltage#Separated_or_safety_extra-low_voltage_(SELV)

In my experience, supplies and systems that meet 60601 have the power supply output ground firmly bolted (literally) to the earth/chassis ground.