If I correctly understand your issue, you created an animation but then had to reposition the whole animation, and the way you did that was by parenting it to an Empty and rotating the Empty - but now it's inconvenient/confusing when editing because the coordinates you see in Edit Mode and Object Mode don't match (even when the Median Point of the selection is the same as that of the Object Origin).
Why this happens
This is a result of the coordinates now being dependent on the Empty. And while we can view the coordinates of the median relative to the World (Global) or relative to the Object container (Local), there is no option to view the coordinates relative to the Parent.
A possible solution
(Save your file before proceeding)
With only your torus Object selected:
Object > Animation > Bake Action...
You have some options to choose from:
Here's a summary of what the options mean:
- Only Selected [only do it for the object(s) you have selected]
- Visual Keying [re-keyframe it just the way it looks]
- Clear Constraints [removes constraints once finished]
- Clear Parents [removes parenting once finished]
- Overwrite Current Action [change this keyframing, don't make a separate action]
This will recalculate the keyframes based on the object's visual position (meaning the data will reflect the way it looks, taking into account the effects of Parents, Constraints, etc).
After baking, you may end up with more keyframes than you need. You can use your previously saved file as a reference of which keyframes were your originals and delete any you decide you don't need.
In any case, after doing this you will no longer need your Empty, and your coordinates will appear as you'd normally expect them to in Edit Mode. As you can imagine, this can be a fix for many similar situations, not just your specific case.
Recreation of your .blend here:
The result after baking the animation: