there is no reason why you couldn't have a boyfriend (whether he's independent or greek) and be an active, enthusiastic member of a sorority. yes, joining a sorority is a good way to meet lots of people, including guys, but you are not required to hook up with them and no one will expect you to if you have a boyfriend
most girls in my sorority would love to have a long-term boyfriend and are just waiting to meet the right guy.
some people will say that being part of a sorority will occupy all your free time & you won't have time for a relationship, but i don't really agree with that. you can make time to do both if both are priorities in your life.
i do think that a greek boyfriend would be more understanding about your sorority obligations, since independents just don't know what it's like to make such an intense commitment to an organization. but, that doesn't mean that an independent guy can't date a sorority girl happily & successfully if both are understanding of the other's situation.
also, about sorority girls not wanting non-greek boyfriends--it's just kind of a "snob" aspect to sorority life. as a sorority chick your social circle will be mostly the greek world, and some girls will look down on guys who aren't part of a fraternity. on the other hand, your sisters will be impressed if you snag a guy from a top fraternity.