Not unusual to find that local authorities have little or no understanding of current legislation, or implement it incorrectly.
The key to the discount is being enrolled on an 'approved' course of study with an approved provider. Students training with the big FTOs, and living within the local authority area of those FTOs, can reasonably expect to receive their discount with little or no problem at all.
If however, you live outside of these authority areas, or are training with a smaller FTO, you may well have to appeal the decision as your council is unlikely to come across this type of training on a regular basis.