This question can be easily answered by noting that "human-measurable" scales regarding direction don't get any more precise than a 16 point compass rose. So direction in this case, is only accurate to within +/- 11 degrees.
You made that claim -- you didn't actually substantiate it. But that's irrelevant anyway. If something's not
the same, then it's not the same. Stop pretending that "close to some arbitrary measure of closeness" equals "the same".
If you had just said 3 degrees off or whatever, then we wouldn't be having this argument.