Nomesorah, while there is a small distinction, it’s not as stark as you describe. Having non frum teachers is very bedieved, and only as a matter of last resort. Go ask any menahel about who they choose for English teachers – unfortunately good frum English teachers (for boys’ schools) are rare.
The heter for having such teachers is that they’re in a jewish school and are accountable. They’re subordinate to the guidelines and standards of the school, although i know many, many students who were influenced regardless. I know of a certain English teacher who convinced many boys to go to college against the wishes of their parents and rebbeim, and that’s just the tip of the iceberg.
Here, there’s no one on top of them, as the situation was described as a non-denominational group of kids, some happened to be frum, some weren’t, and there’s a coach who will say heaven knows what to the kids. He might use foul language. He might shmooze with them about girls they have crushes on and encourage it. That’s just the first two examples that come to my head.