The original post is very unclear. Might the scenario be as follows?
A child sat the Slough exam and got a good score (= child "who qualified in exam").
The parents did not name the school on a common application form at the end of October; possibly they didn't submit a CAF at all (= "not opted in CAF form").
In March, the child was not allocated the school for which they had a good enough score. Maybe they got no school (no CAF = no state school); or perhaps they were allocated a school they didn't want or even list at all. [Btw, that is what happened to 150 children near us in March 2015].
After some discussion, the parents realised that their child's Slough score would have been enough for a selective place IF ONLY they had applied for it by naming that school on the form.
The parents asked to go on the waiting list for the selective school (= "request").
The child's score put him/her at or near the top of the waiting list.
They were offered a space when someone else turned down a place (= "place was offered on request").
I like my Shades of Educational Skulduggery scenario better, but your suggestions are probably more likely
Perhaps the new day will bring enlightenment.