Well, for the most part, we technically are secret societies. It's not a good or bad thing, it's a fact. A lot of it is just press and perceptions, let's face it, the negatives sell. What is more newsworthy? ABC raises $500 for the local elementary school's library or ABC members did something stupid at a campus party.
Our Greek Letter organizations do have secret ceremonies or traditions which bond our members to one another. The only exception I can think of is Delta Upsilon.
FWIW, even my academic honorary's induction was "secret". I met the qualifications, applied for membership, and was selected to join. Actually it was a very similar process to sorority recruitment, only the overall GPA/departmental GPA and involvement requirements were much stricter!
Whether we like it or not, there is an element of exclusivity in GLO membership. If a Potential New Member or Candidate does not meet the GPA or course load requirements, they cannot join. If they cannot meet the stated financial obligations, they are unable to join. There is an element of exclusivity though for dozens of other recognized student organizations. Want to join the dance team? Well, not only do you have to be able to dance, you have to be able to dance a variety of styles well AND tryout AND be picked. Want to join the debate team? College Republicans? Exclusive? Yep. That's the real world