Thing is, given that HB & HG is presented as a work of historical research, surely Brown is just supporting that research by writing a book that assumes their research is correct?

If they're arguing that he ripped off their ideas, aren't they arguing that their book's not true? 'Cos if their book is true, all he's done is written a fictionalized version of real historical events, and you can't claim history for yourself. OTOH if HB & HG is complete bollocks (which seems, on the face of it, more likely) I suppose they might have a case....