To be fair to the female switchboard operator: Many organizations instruction their operators to avoid engaging in conversations or exchanges with callers beyond finding out who they want to talk to. It is usually a maxim of such organizations or companies to warn operators that callers may be trying to extract any kind of information from them under the guise of "innocent" questions. Call it paranoia but I prefer to think that JW organization is simply following standard organizational protocol for its operators.
I'd be more impressed with the OP if the caller had been put through to someone else in the organization besides the operator and had the exact same exchange.