I don't have a definitive answer as to why some coaches don't post stats, but I've never been told no when I've asked about them. Every coach I've ever interviewed about their next opponent knew what player(s) needed to be stopped, who led the team in scoring and so forth, whether stats were posted or not. Game films, assistants going to scout upcoming opponents, or the coach themselves, coaches always seem to know about the next team they play.
Our coaches use a tablet to take stats at the game, they connect to the internet and by the time I get home to write up the story, the stats are already on Max Preps most times. One coach I know will post the stats from the tablet as kept by the student assistant, then he will watch the game film and keep stats himself, and repost any corrections, but he's a bit of a stat junkie like me. I've never been asked by any coach, Chillicothe or opposition, of any sport not to post stats on my website.