Thought.. Well actually MEMORY. that MIGHT apply.
A few years back the Trailer next to me (30 amp) had no power.. Well after much testng we had good power to the outlet but none to his RV.. Turns out the blades on the plug were a bit...er.. short. and did not contact the contacts in the outlet. I dug in my adapt-a-kit and found a 30-50 dogbone.. Blades made solid contact with the 30 amp outlet on the bone. (I could feel the contact point about half way in) and the 50 worked fine in the park's 50 outlet he had power.. Well. I got sick and did not set foot outside for the next few days but when next I went out he had his own bone and mine was on the seat of my towed which was not locked.
How this applies:
You measured 120 volts either side to center on the outlet (good)
But did you measure the depth of the contact?
And is it possible one of the contacts in the outlet is "Spread" to the point it's not contacting your plug?
Have you tried a DIFFEERENT 50 amp outlet?