Unless things have changed since my collegiate days, ours is not "open", but may include "invited guests". For example, our (non-member) house mother regularly attended, and sometimes mothers would attend if they were local.

I think the idea is more to protect the solemnity than for it to be actually secret. After all, your pledges are not initiates yet, so by including them in a pledging ceremony, you are, by definition, revealing secrets to non-members.

^^^ Thanks for the clarification. I was trying not to make assumptions or put words in anyone's mouth.

Hit the nail on the head!
Thanks AlphaFrog. "Not initiated yet"! That is the key!