The ground wire of the probe on a regular oscilloscope is connected to the outlet ground.
Connecting the two grounds together is not about the signal, though.
The oscilloscope ground is connected to the outlet ground as a safety feature. The point of it is to keep any uninsulated parts of the scope from killing you.
You can (but should not) disconnect the ground pin of the oscilloscope power lead, and the scope will work properly. The metal housing and any exposed metal parts will be at the same potential as your circuit though. If you connect the probe ground clip from the scope to a high voltage source in your circuit, then the high voltage will be on the housing or other metal parts - just waiting for you to touch them so they can kill you.
A scope without a grounded power lead (USB or battery poweted) must be double insulated so that you cannot possibly touch anything that may have high voltage on it.
When you connect the ground clip from the scope to the device, you are providing all the ground that the signal requires.
All an oscilloscope does is to show you the voltage difference between the probe tip and the probe clip. An ungrounded scope can measure the voltage between any two points in a circuit. A grounded scope can only measure voltage between the ground (connected to the power lead ground) and the signal.
All you need to measure a voltage is two points connected to the circuit. To safely measure potentially high voltages, you need either a grounded scope or an insulated and isolated scope.