I would first like to know what is the probe impedance i,e if you are using a 50Ω or 1MΩ probe, hopefully if you are using a 1MΩ probe you might want to check your what is the impedance setting on the oscilloscope impedance (50Ω or 1MΩ).
The most likely explanation for blowing the 51Ω resistor would be, the setting on the of oscilloscope would be 50Ω, so now the total resistance between the Hot and neutral will be 150Ω, hence the current flowing thru the path is 240/150 Amps. I assume that the resistor are SMD which are rated for 1/8 W, which would not be able to handle current more than 1 amp, hence blowinng the resistor.
I wonder what kind of power supply design uses 51Ω, unless it is a RF circuit, I have never seen a power supply terminated in series with 51Ω, so you might better recheck the design.