If a man told me he never fukced a woman on her period I'd wonder what's wrong with him. I lived with a handful of women for years at a time. Period ain't stopping shyt. In fact, if she's fertile, that's a good time to shoot the club up (if you're trying to avoid pregnancy)
If a man told me he ate the box while she was on her period, I would consider him a maniac.
Here's a caveat. Eat the box with a fresh tampon in. That works fine.