I checked on these bug numbers again. All three have both been marked as-designed (two in July 2016 and the other about a year ago) with this statement in the 2nd one: "The ECW sdk has been updated, to take the projection information in the dataset and use that. This was not being done in 10.2. Hence the prj file is not used but instead the projection info in the dataset is given precedence. This is as designed."
By SDK, I assume that they mean the code that handles ECW as a raster type. So if there was a discrepancy between the internal coordinate system/georeferencing information versus the external (prj file and world file?) that could be where the offsets are coming from. If you have ECW and you're sure this isn't the problem, contact techsupport again, reference the bug numbers and say you think there's a different problem.
Melita