How do appeal panels know that the stuff that is being given to them is genuine? Does it have to be on school headed notepaper?
Panels look at all evidence submitted, but it's down to them to decide how much weight to give to any one item. A letter on plain paper could be from anyone, or indeed, forged. Therefore a letter on headed notepaper will carry a lot more weight, be it from the head or the class teacher.
I can't see for the life of me why some heads are like this but some are, even in areas peppered with state grammars.
I can. If a head writes a letter of support for one child, but not for another, the parents who were not supported may well be angry. What if they have a younger child at the school? What if they're a parent governor and want to get their own back? Some schools have a policy of supporting all appeals, but the letter is exactly the same for each child, so will prove pointless. Others do almost the same letter, but a panel may read through the lines and notice that one has slightly different wording - but even then parents may compare their appeal docs (leading to the same possible angry parent problem). The other option is to write no letters of support.
Panels are very well aware that many heads take that route and do not favour appeals who have said letters. Most useful to the panel are CAT scores, SAT scores, Reading Age (although different schools have different tests, so you may have a top score possible of 12 1/2 where another schools top score possible may be 15 years), and any other academic evidence (rather than 'Johnny works very hard in class'!).