It's "trained in", not "born in" to be homegrown.
You'll have a moderately hard time getting South Americans in on transfer under the age of 18, though, which is what you'd need for those to eventually qualify as home-grown (at club). Getting work permits is tricky, and for Argentina, they can't leave until they're 18.
Anyway, the EPL rule is not 4/8 of UEFA that you cite, it's just the 8 part: 8 players who have been registered for a total of 36 months or three entire seasons with any club in the FA (or, I believe, FA of Wales) before the end of the season during which the player turns 21.
What FM doesn't get right, yet (that I've seen anyway) is for the UEFA homegrown rules to reflect that time spent out on loan deducts from the time grown at club (or so it's been explained to me in the case of Ryan Bertrand who doesn't count as home-grown for Chelsea for this loan reason... none of the wording I see in the rules themselves seems to make this explicit).