In what case would dark rum not be kosher?

Dark rum would not be kosher if non-kosher wine could be added during its production process, which aligns with the correct answer. The kosher status of beverages, especially alcoholic ones, is influenced significantly by the possibility of non-kosher ingredients being mixed in. In this case, wine is specifically mentioned because it must come from a kosher source, and the practices surrounding the production of wine are stringent in Jewish dietary laws. Since wine can influence the kosher certification of a product, if it is included in the rum, it would render the entire product non-kosher.

Other factors such as mixing rum with fruit juice, the brand of rum being imported, or aging time do not intrinsically affect the kosher status of the rum if all other production practices adhere to kosher guidelines. While specific conditions might influence the kosher status of a product, they do not fundamentally alter the rule concerning the inclusion of non-kosher wine.