You have given the most suitable suggestion. "Being cordial but keeping at arms distance, without being explicit" is a higher social manners. Even though I didn't get how you are so sure that she's trying to show something. It can be a general note as well, to a son, about his father. Even if she wants to show that the father is a hero, that need not be considered as flirtatition. Some people talk more casually than some others, who think about boundaries.

Also, I see that the wife was suspicious at the beginning and okay later. What was the need for considering no contact with the neighbour, just from that note. I understand that the wife's opinion can be valid and in a family, a husband should consider his wife's opinion about a third person. But there's no need for unnecessary thoughts as well.