[snowman]

Must be some kind of funky tester to indicate what yours is doing. To get this indication your tester should be seeing a voltage between the neutral and ground, not good.

Forget the tester, use an ac voltmeter. First check the ground like I suggested. Do not skip the continuity to the water pipe check, its absolutely necessary. This test will verify that the hot is or is not reversed, no if ands or butts about it.

And yes they can be reversed and work for fourty years without apparent problems especially if the neutral is open. Very dangerous situation if true. I have seen this in the bathroom of a house I flipped last year. To make matters worse they had wired an extra outlet in series with he miswired one and connected the switch wrong. Plug a vacuum cleaner in the hallway and the bathroom light came on! The ground wire was there, but it wasn't connected to actual ground. If some had grabbed a "grounded" piece of equipment and a water fawcet at the same time they would have been fried. fortunately many bathroom appliances do not depend on a ground connection and are double insulated instead.

You can keep tightening your connections as long as you like but the danger of fire will still be there and it can happen at any time. Very bad advice to continue down this path, kinda like smoking while you fuel your car, you can go for years without any problems.