There is no right to see evidence before deciding whether or not to accept a fixed penalty. Your friend may be able to see it if the police feel so inclined (though they usually are not) but he does not have the right to do so. This has nothing to do with the Data Protection Act.
The idea of a fixed penalty is that guilt is admitted and the penalty paid without the need for administration. If, as you suggest, he was not disorderly then he should refuse the offer of a fixed penalty and instead opt for a court hearing where he should plead Not Guilty. A trial will then be needed and he will be given all the evidence against him.
If he is found guilty it will cost him considerably more than the fixed penalty.