I don't know if this will help but check out this
thread and look at #58 on page 6 for what I found to be the problem.
I have found wiring like that more than once, a long time ago, back in "99" or "2000" I posted about a lady who was getting shocked off her refrigerator, in the garage on a concrete floor, I tested the plug like you and had the correct lights on my 3-light tester light up, so I got out the wiggy, and same thing, voltage between hot/neu, and hot /ground, and nothing between neu/ground, also showed continuity between neu/ground.
I said wow how is this possible, I read the ground prong of the fridge to the frame of the fridge, and it showed continuity, so I ran an extension cord from a known good receptacle (one I temped into the panel) to the location, and sure enough it showed the neutral and ground live, and the hot was dead, looked in the receptacles but there was no jumpers, ok got under the house, traced the romex ( was new) to a junction box, where it was fed with an old cloth covered romex, even the conductors inside was cloth covered rubber, and you couldn't tell which was the neutral or hot, it was here they had connected the EGC to the neutral to what they thought was a neutral conductor, it wasn't it was the hot, after explaining it to the home owner we rewired the whole house removing all the ungrounded romex, we found several other places like this, but it was in the house so there was no concrete floor to create a return path, but dangerous just the same.
I have used an extension cord to a good receptacle ever since. one of the best ways to trouble shoot stuff like this.
