0.27mA could burn some sensitive components 🤔
The voltage could burn some if you are not cautious, depending on how you connect it. But so would static electricity (fingers).
Let's compare the 2 situations:
Suppose you do not interconnect - and earth ground on the PSU (meaning: leave as is):
a) If you use the PSU to power your circuit, and you use the scope to measure between - and some signal in the circuit: the - will connect directly to earth ground (through the scope). Without going through any of your components. So all OK.
b) If you connect the gnd of the scope in other places, you MIGHT hurt some components. So bad idea.
c) If you have multiple power supplies that you use to create multiple input voltages: there is no problem as all will be floating from earth ground.
But now suppose you interconnect - and earth ground on the PSU.
a) If you use the PSU to power your circuit, and you use the scope to measure between - and some signal in the circuit: you will have created a ground loop. And since it is low impedance, you can create dangerous currents. So you MIGHT hurt some components and instruments, or even yourself. Bad idea.
b) If you connect the gnd of the scope in other places, you WILL hurt some components, as then suddenly you will have created a short to -. Bad idea.
c) If you have multiple power supplies that you use to create multiple input voltages: huge problem, sparks etc. Bad idea.
Conclusion: bad idea to connect PSU - to earth ground.