Even when it's midnight and the clock hands point to 12, it's just 0:00 in our heads. Of course when thinking an talking about time, sometimes the numbers 13 to 23 are replaced with their 1 to 11 counterparts and if it's ambiguous, a "in the morning", "in the afternoon", "in the evening" is added. But there's a clear distinction between "0" and "12". When someone says "12 o'clock", it's always 12 noon and never 12 midnight, since that would be "0 o'clock".