No this is not a rule at all. If you are carrying them for your wife who is clearly right next to you, then you are fine. GA was being overly-paranoid by far.

If it was clear you are traveling by yourself then yes obviously she is right, however if you are right next to your wife like that and she is empty handed, you would be fine.

Think of this scenario, let's say you are traveling by yourself and get scanned with one roller bag and one backpack in compliance. Then on the jet bridge, when the line backs up, you pull a 3rd smaller bag out of your backpack. There is zero way the airline can be liable for that as they would have no way of knowing.

As a former airline worker I assure you that GA was taking a rule and overinterpreting it. Now had you guys had more than the allotted bags and they let you go, if the FAA saw it "technically" they could get fined, but that's extremely unlikely unless it was a habitual habit by the GA who had been talked to before.