The voltage between two legs of the stator is determined by the how many windings are between them. What they DONT care about is if other chunks of metal are touching the windings at points in the middle (which is just a multi-tap transformer). So, a stator shorted to the housing (not shorted between windings) will still produce AC voltage between the legs even if there is contact between the windings and the stator body.
I bet if you check for AC current between the unplugged stator leads and the engine you'll see at least 20v when revving.
Which brings us to the rectifier. Once the rectifier is plugged in to the stator, it adds a SECOND path to the engine via the wire to the negative battery terminal. The voltage that would normally be forced "backwards" through the battery to charge it can now avoid the battery and flow directly back to the short in the stator windings. I don't know exactly what that would look like as far as voltages is concerned, but it's definitely mixing the AC and DC side of the rectification circuit, which is not good.
Since the ohm readings between the leads and ground are practically the same for each lead, it may be the center splice of the windings may be shorting to the stator body. If so, it may be possible to fix the stator by adding insulation between those two electrical components without having to rewind/buy a new one. Still a PITA though.