The list of excluded train services includes all relevant services which run from London mainline termini. So, for example, Hull Trains is included because they operate out of Kings Cross. There is clearly no point in mentioning, say, Arriva Trains Wales, since they don't operate services within the London area.
There is no such operator as 'West Country Trains'.
Here's the information you're really seeking:
http://www.nationalra...s/london/freedom.html
Chris