I was going by heart rate since you mentioned the Polar heart rate chest strap.
Polar app might say 500 calories (the strap itself doesn't tell you calories burned).
Treadmill might say 200 calories. Endomondo might say something else. MapMyRun might say something else. The bike at the gym might say something else. The Watch might say something else.
You're gonna return the watch because the calorie count on apps differ?
If you (or your wife) knows that she was in the heart rate training zone for X minutes during a workout -- then that should be what matters most. Who cares what the calorie count on an app says? They're ALL estimates and they're all going to be different.
Is the calorie count always doubled on Polaris? Because sometimes third-party apps get confused by the HealthKit import vs. a proprietary process and double-count things.
If, for example, MyFitnessPal were configured to get data from both HealthKit -and- straight from Polaris (not sure if there's a bridge there, but if) then it might doublecount the calories.