The linked to debunking was certainly interesting but not entirely sure what it debunks.
I haven't read the statute in question. It isn't clear to me who to believe in terms of which child care facilities fall under its domain. I would suggest that were there is doubt, ordinary citizens tend to assume for good reason that the statute covers even if it gets interpreted not to.
But school employees who are tasked with enforcing school rules are typically understood to be, legally, agents of the state. They are state agents, and therefore what goes on in a public school brings the state into the childrens' lives. This is important in areas like search and seizure law regarding public vs private schools. The private school might be able to claim some parental authority in the absence of the parent's presence regarding searches and seizures, but a public school is subject to the 4th amendment. So I don't think it is unfair to say that this was done by a "state agent." However calling the individual a "federal agent" is pretty clearly unfair. The only one who did this however was Limbaugh and I don't know anyone who listens to him seriously.
Secondly nobody really disputes that the facts of the girl being offered the full cafeteria lunch in addition to what she had brought from home. The question is whether this was a functional replacement or a functional supplement. That's a question that hasn't been adequately addressed yet either.
As an interesting aside, I note they require meat and dairy in the same meal. What happens if the family converts to Judaism?