>Yes, that is true, I can't dispute that even in English, the word can have different meanings. Personally I would still include it, mainly because it is a frequent cause of translation errors - one of the most frequent, actually. Well, just consider this my personal preference.
Actually you're right - because it does constitute a false friend pair: not only (US) billion means a milliard elsewhere, the (rest of the world's) billion translates as trillion here. Since it goes both ways, it is a false friend.
Included and updated.