[thebabayaga13]

So, for missing item, i would say i got the Ring Box but no Ring inside it? or say i didn't receive anything (the box or ring) 

Both are equally effective.

The former comes down to a manufacturer error, and the latter Is a warehouse error.

I assume if i go with missing item method will have a less chance of carrier investigation

Correct.

It's not carrier-related.

Thank you, always appreciated!