What do you mean by "if a school doesn't ban AI that does not mean they're forced to use it"? That's not an argument anyone is making. People are saying the turning off search capabilities just because the school opted out of AI is petty. That's exactly what they're doing and here's a quote from the article saying that:

“Search and A.I. are deeply integrated,” said Chris Phillips, vice president for education at Google. If a school has banned A.I., he added, students “will not have access to search, and they’ll see a message from their school that indicates it’s not available.”

I hope schools keep the AI off and switch to a different search engine.