Indeed, the crank face is flat. On the left side the extractor is fully inside the crank hole and perpendicular to the crank arm and bottom bracket spindle).
Once the LBS wanted to unscrew it they were also surprised how it looked like and thought that the thread was cross-threaded. It was a bit harder to unscrew from this side too but once unscrewed we verified the threads on the extractor and it looked really OK, also it was very easy to tighten it back. So they said as it looked like the hole in the crank was drilled not super precisely but at the end it's not an issue as threads are fine and should not have any impact on how the cranks work.
As you said, this is very expensive stuff and I have to consider that maybe they just tried to hide they mistakes when they mounted it in first place.