Yes, you are correct, they invited her to wear a brooch in the shape of a cross.
I give you that.
However, I do not understand why the necklace was not allowed.
The overly PC explanation of it being “dangerous” does not ring true.
In any case, I do fully respect the rules a school sets but we should not be so rigid as to forbid a discreet necklace.
But .. in fairness to you.. you did correctly point out that the school does allow crosses, albeit in the shape of watches or brooches.
This is a point a lot of us posters (including me) missed.
So, mea culpa!
Maybe the thinking is that when the children are playing, the chain on which the crucifix hangs might catch on something and injure or, in the most extreme case, strangle the child.