Actually, your first sentence is the correct one, no dialog is recorded on the set (no sync sound); this does not mean there is no sound at all in the finished edit.
In scenes such as this sound becomes
more important.
Sounds can be extremely evocative during scenes like this; you can exaggerate sounds and use them to highlight actions. Maybe instead of merely setting the ring down she she drops it and it bounces, then spins for a moment; this is what captures his attention. If you have a close-up of this (slow-motion?) you can really play with the sound here. This now focuses the attention of the audience upon that action, and the meaning and importance of that action is highlighted.
Here you can use the paper to give more emotions to the scene. The newspaper is first a boring familiar sound, then can enhance the husbands anger/surprise if lowered forcefully. How he folds it - slowly and neatly or forcefully and angrily - enhances his reaction and tells the audience more about his character and how he may deal with the situation.
In your beats almost total silence or exaggerated ambient sounds (a ticking clock, for example) will highlight the tension between husband and wife.
All these "small" sounds, by the sonic focus given to them, replaces the dialog to a degree and become, in essence, minor characters in the scene. But you need to think about it and plan for it before you start shooting so the sounds can be used to greatest affect by the sound editor(s) and mixer(s).
One of my favorite films, "Forrest Gump," uses sound in this way all throughout the film. In the scene where young Forrest runs from the bullies on bicycles and his leg braces come off the sounds of the braces breaking apart are greatly exaggerated. In the Viet Nam rain sequence the rain sounds very precisely echo Forrests description of the rain, and in the battle scene the weapons and other war sounds are all from Forrests POV. In fact, the entire film (with the exception of the Jenny scenes) is entirely from Forrests point of view, and Sound Designer Randy Thom (one of my heroes) discussed the use of POV sound extensively with Robert Zemeckis prior to filming. I love all of the films on which Zemeckis and Thom have collaborated because of the wonderful use of sound in all of them (Flight, Polar Express, Forrest Gump, Contact, Cast Away).
Just for fun, the "history" of the term M-O-S; Mit-Out-Sound:
http://en.wikipedia.org/wiki/MOS_(filmmaking)
http://filmsound.org/terminology/mos.htm