почему "ЗА время обеда он не говорил ни слова", а не "ВО время обеда он не сказал ни слова"?

See a translation

"ВО время обеда" sounds like some particular situation occurred while the person was having a lunch. And "ЗА время обеда" here sounds more natural because it has a nuance in meaning that in this case we take into account the WHOLE time of having a lunch. Like - he didn't say a word through ALL the time of the lunch.

For example, to feel this nuance of difference between ЗА and ВО better:
ЗА время, что я путешествовал за границей, дома ничего не изменилось. - During the time I was travelling abroad, nothing has changed at home.
ВО время путешествия за границу я сломал ногу. - While traveling abroad, I broke my leg.