I agree with my sorors -- go and do your thing in the community of interest. We have ways of observing interested people.
Having said that, I've seen interests attend our two major events (our debutante ball and scholarship breakfast). They generally are invited by friends of theirs who are sorors, and I haven't seen groupie-esque behavior. I guess that reflects the fact that Greek life in my corner of SoCal is very stealthy.
If it's a public event, I don't mind seeing an interest there, but I don't like groupie-esque behavior, sweating people, etc.
As for the San Diego NPHC picnic, most of the independents I have seen are significant others of Greeks, some of whom are not interested. That's a whole different matter.