The agent appears to be correct, this is the official text from Hilton:
https://www.hilton.com/en/hilton-hon...-elite-members
2nd Guest Stays Free: A guest stays free in the Member's room on qualifying stays at hotels when there are additional charges for double occupancy. This benefit excludes stays at any hotel when the rate includes additional components (e.g., meals, activities, parking); specialized rates (e.g. package rates, bed & breakfast rates) or taxes that are quoted as a per person or per room charge; or is an All-Inclusive property.