BILINGUALISM AND CULTURE

I intuit that for the average language student, bilingualism refers to the mastering of two languages, right? "In my book", the definition is amplified, engulfing culture as well. And by "culture" I refer to history, music, religion, philosophy, or, in short, the framework of a person´s intellectual baggage which must be duplicated or mastered in the two languages of the true bilingual speaker. If we talk to a Spaniard about Alexander the Great, we must say Alejandro Magno. Saying Alejandro el Grande will sound weird to him. If a Spanish-speaker talks about the Las mil y una noches, he should remember that The Arabian Nights will be more comprehensible to the English speaker.  El lago de los cisnes turns into Swan Lake, as The Flight of the Bumblebee will be better understood than El vuelo del moscardón. An Englishman should not quote The Merry Wives of Windsor and instead mention Las alegres comadres de Windsor. The British cross the English Channel whereas Spaniards cross El Canal de la Mancha. El peñón de Giblartar ends up being The Rock of Gibraltar. I pose that the true bilinguist must be able to carry on a conversation in either language without giving away he speaks the other. A tall order and quite a feat, granted, but a feat that we must all aim for.