So the answer is... and it's a little embarrassing...
is fine, fridge works and internal wiring polarity is correct.
With some more fiddling I realized that the GFI circuit on my house receptacle was tripping, but only occasionaly. So I could test for power at the end of the extension cord and confirm power. However, the next step of plugging in the fridge apparently wiggled the extension cord enough to trip the GFI. Turns out the extension cord was bad - probably a small and inconsistent short in its internals. I replaced it with a different cord and all is well. I'm not an electrician, but I'm guessing that the same current leakage that was periodically tripping the GFI was also confusing the polarity tester into indicating a reversed polarity.
So as an early poster postulated - often its the simple things.