Tarzan was played by a guy called Jock Mahoney - an American. Hollywood has this annoying habit of simply appropriating folk heroes (or otherwise imaginary ones even) from other countries and making them American! Tarzan, as envisaged by his creator, Edgar Rice Burroughs, was English - an English peer, to be precise. Tarzan, Lord Greystoke. He wasnt meant to be American, just as Robin Hood wasnt meant to be American either.
I mean, Robin Hood is synonymous with English folk history. Americans dont HAVE anything - or anybody - approximating a Robin Hood (or do they?). I quite like Kevin Costner and I quite liked the movie "Robin Hood, Prince of Thieves" as well... but the fact remains, they werent supposed to be Americans! Oh well, I guess Samuel Taylor Coleridge's words still stand true - to enjoy some things, to go into the realm of fantasy, a "willing suspension of disbelief" is very necessary.
PS. Ok, I HAD to bring in a literary angle! I mean, I graduated in English Literature, and what use a "classical" education if I cant introduce a classical allusion or two into my writing, huh?

PPS. "Tarzan Goes To India" is worth it if only to look at the baby elephants... man, those li'l babies are soooooooo damn cute!