I still wouldn't rule out the Bucks end of things either! I have come across some administrative issues with both the Appeals and Admissions team there, so I suggest that she writes to the Admissions team asking them to actively
review the case from their side and confirm their view in writing. If the child has passed the Bucks 11+ they DO have some record of him somewhere! (It may not be of an application for a school, of course.)
However, names can be entered into systems wrongly, files can be mis-filed and people can just mess up.
I think the fact that the school has kept a copy of the preferences is quite interesting. Perhaps it is standard procedure in Slough, but it certainly isn't in Bucks. We get a "yellow reply card" to send off, that wings its way back a while later.
I think that if your friend can pursue all three elements of this - school, Slough LEA and Bucks simultaneously, she may get to the truth more quickly, which will put her and her child out of their misery sooner. (Sorry - can't remember from the other thread if it was a boy or girl - I suspect girl?)