A few episodes earlier in "The Deadly Years" we know the Romulans had broken "Code 2" communications. It wouldn't be hard to imagine that they got their intel on the Enterprise and Kirk from that episode. The spying of course still could happen but that would probably come from the merchant ships crossing the zone to pick Romulan Ale
Interestingly enough, the Romulans contact the Enterprise with a "Class 2" communication (is that same as "Code 2"?) in "The Enterprise Incident".
Very good rationalization! Just "bought" it.
Let's keep this dialogue in mind: "The treaty, set by sub-space radio, established this Neutral Zone, entry into which by either side, would constitute an act of war. The treaty has been unbroken since that time."
Sounds like an armistice to me, and I believe the "Neutral Zone" was inspired by the Korean Demilitarized Zone
. There are just too many analogies to recent events (then) in "Balance of Terror" which I find difficult to ignore. But that undoubtedly helped to create credibility on behalf of Star Trek, because audiences could relate to these things back in the 1960's.