Their evaluative ranking in the arbitrary categories "classics", "greats" and "masters" is my choice : the general consensus from their mentions in lists with my own appreciation weighing in. My entirely subjective choice would drag Hollywood much lower than non-Hollywood auteurs across the board, as I disagree with this consensus. The outdated classicism of Eastwood and Gray don't match as high as the achievements of 50ies Hollywood auteurs, who, in turn, are outclassed by today's World auteurs standards!
Conclusion : it's not the Hollywood system that makes great auteurs, it wasn't back then, it's even less true today. It was just a coincidence if these artists happened to be there (World War II helped to attract "European brains refugees" in Hollywood!) and if there is a higher density of filmmaker population working in Hollywood, statistical chances to find great people among them are higher than anywhere else... especially back then, when the idea that making films outside the studio system was only marginal and unpopular.
Even if MY ranking is partial... I doubt anyone would suggest that the best people working today within the Hollywood system are as good as the auteurs cherry-picked by Cahiers in the 50ies!
Please stop confusing auteurs with the industrial conglomerates funding them.
See also : Hollywood or not Hollywood (Cahiers)?