Here's what's actually going on inside those 3-light testers.
You see there is a neon light between each of the prongs. The red is between neutral and ground for instance. The problem is, neon lights are not voltmeters. They will light for a wide variety of voltages, and won't tell you which voltage except very subtly by brightness.
When they wrote the descriptions for the device, they were forced to come up with something for every light combination. They were optimised for the kind of mistakes seen in new construction... and so they're misleading and wrong when troubleshooting old work. They're so horrible I call them "Magic 8-ball testers"*. The testers are much improved by tearing the sticker completely off, and learning to interpret the raw data the lights are providing.
For instnace, a broken neutral with a load on the circuit turned on. Neutral is pulled up to 120V, so the outer lights light. Interpretation: "Hot Ground Reverse" (unlikely). We've had novices waste hours trying to chase that nonexistent fault.
The ground-neutral tangle is a clue
If the green/ground wire is connected to neutral in any way, That Is Bad. That is often done by incompetent hacks to try to work around a problem, typically one they created.
I suspect that somewhere upstream, the neutral wire is broken. The previous hack decided to bootleg neutral from the ground wire, which is why he crossed them.
Generally, wiring problems are at terminations, and every one of those should be accessible. However every once in awhile you have a problem with the wires proper, e.g. someone drives a nail through a misplaced piece of Romex.
* Amusingly, the randomly assigned Imgur URL for this is 0BSoD.jpg. I couldn't make that up...