While those rings might look absolutely identical, they’re not. Several expansions ago Blizzard switched away from having different versions of the same item (e.g. completely seperate items for normal, heroic and mythic) to using one item and attaching so-called “bonus ids” to set the specific item level, difficulty text and more.
You can see those bonus ids at the bottom of tooltips on AMR which look like that for your two rings:
Equipped: bonus ids: 1487, 4786, 4822, 6515, 6516
Inventory: bonus ids: 1487, 4786, 4822, 6513, 6516
AMR has to look at those bonus ids to determine exactly which item level etc. your specific item has and due to the fact that there is no documentation on bonus ids and its often not clear why specific bonus ids are used at all, errors like that may occur on AMR if they’ve never encountered that specific situation.
If even one bonus id is different, then two items may have wildly different stats (see bonus id 1512 vs. bonus id 1627 for example). For that reason AMR currently does not recognize your rings as “identical” and might recommend changes - although that generally shouldn’t happen for a change of 0,00%.
The AMR team has been quite quick fixing those inconsistencies in the past, so I guess that specific example should be fixed soonish too - now that they know about it.