You've raised some important issues that any Beta Sigma Phi chapter that operates on a college campus will have to consider.
Two immediate thoughts...
1. I love your honesty. You've really had to think about
why you desired a sorority experience from the beginning, and
how BSP does or does not meet your needs. I'm glad that you've grown into a mindset of seeing BSP's differences and embracing them. But wouldn't you say, at its core, Beta Sigma Phi is about building relationships with sisters while developing as an individual? Not so different other sororities (both collegiate and community-based), right?
2. I'm a bit shocked and a little hurt (on your behalf, I guess

) by the potential new member's comment. How very forward of her to say you are a BSP because the others "didn't want you." That makes me cringe. Would she go to a smaller NPC chapter and ask a sister if she is an XYZ because they were desperate for members? Seems like the same thing to me.
So...my advice...hmmm...
First off, every sister's journey to Beta Sigma Phi is going to look different. I started a chapter as a graduate student. It was not officially "on campus," but only two of our members were not students at that campus. I knew that our chapter wasn't going to look like or operate like an NPC, and I was glad of that since my life as a newly married, full-time grad student, part-time college instructor wasn't going to allow me the schedule of an active NPC sorority member. On the "con" side, I also had to realize that I wasn't going to like
everything about how BSP operates on an International level. In over 10 years of membership, I've been able to understand and embrace those differences, too. Like you said, your perspective changed. That's part of being an adult.
Given that we are all going to have a different BSP story, I would not rule out a potential member because she thinks that Beta Sigma Phi is sort of a back up plan. (I hate the notion, but it doesn't have to be a deal breaker.) She needs to be well informed of the differences between BSP and the other sororities on campus. She should be given a few opportunities to see your chapter in action and get a feel for how you operate from a functional stand point and how you operate as sisters and friends. You might even want to show her
The Torch and emphasize the lifelong opportunities that you can't help noticing when you see the wide age range of our active membership. Give her the fullest picture possible, and THEN she can decide if BSP would only be a "back up plan" for her or if it is a legitimate and exciting opportunity. Just like anyone else, she could make the wrong decision, but that isn't the end of the world. She will learn something about herself along the way. I've had some disappointments in my sorority experience, but I keep building a new and fuller perspective. I don't think that anyone is BORN as the perfect Beta Sigma Phi. We all bring expectations and "baggage."
Even though Beta Sigma Phi is different, if a woman is looking for sisterly relationships, leadership opportunities, educational opportunities, and community service experiences, she can make BSP work for her. If she wants something else (maybe something less tangible), she might need to look elsewhere.
I hope this is helpful in some rambling way.