Try the following measurements:
With your multimeter in DC volts mode, measure the voltage across the terminals of the power supply You should get what you expect from the power supply.
In AC volts modes, measure the AC voltage from one power supply terminal and earth ground. You might see a large AC voltage -- perhaps even as high as 50VAC.
What's going on is something like this:
In the first case you are measuring DC voltage across A and B and you get the expected voltage of the power supply. In the second case you are measuring the AC voltage across B and C (or A and C) and you're seeing the coupled mains voltage.
For a third experiment, put like a 1K resistor across B and C and measure the AC voltage across it. You'll likely find that the voltage decreases a lot -- perhaps down to just millivolts. This says that the coupling (the capacitor) is rather weak.
In the case of your oscilloscope measurements, note that a probe's ground is implicitly tied to earth ground. So if it is not connected you will be measuring between B and C (or A and C). However, if the tips of your probe are connected to A and B you will be shunting out the AC source and only be measuring your power supply's DC output.
Corrections to this explanation are appreciated.