I've been lurking on this thread for quite some time. I think, probably, as in most things, the truth lies somewhere in the middle--neither the individual chapter or nationals is entirely to blame. Perhaps they both just had poor communication.
But, as a woman in a chapter significantly under total, with a repuation very similar to the one that's been described for Penn's Phi Sig chapter, I can understand where they're coming from.
Think about it: Your chapter has a stellar GPA and service record. You are proud of your diversity and acceptance of lots of different kinds of wonderful women. You've got a strong sisterhood--you know and love your entire chapter. Lots of accomplishments in that area. The only area where you lack is in the social area--you aren't known as "popular" or "pretty". You have trouble making quota and are significantly under total (60 instead of 100 (in my own chapter's case, 50 instead of 80)) However, that's just fine with you. Women who buy into the stereotype and don't want to be a part of your chapter because it's "uncool" probably don't belong there anyway.
Now, nationals comes in. They want you to be at quota/total. (You want to be at total too---only you can't seem to get there because of ugly rumors/stereotyping--many people withdraw from rush rather than join your chapter!). In fact, they want you to remake your image rather to help make total. You may not be opposed to this in whole. Except, they want to shut you down! You feel like you could work on chapter image without this step. You are not so far under quota as to not have a functioning chapter! You do not have only 10 women! You have a large and strong sisterhood. In your mind, you might feel like the real problem is your reputation. You might feel like nationals wants to remake you more like the other groups to get rid of your reputation, rather than focus on the positive things about your chapter (GPA, service, diversity, sisterhood, open-mindedness) to get rid of your reputation. Whether this were true or not, you might be insulted and hurt.
That is the perspective I would take on this issue. I really feel the Penn chapter's pain, because my chapter is so, so similar (although I think our reputation is slowly improving as we do focus on the positives, and we have not been threatened with a shutdown). At the same time, I do not believe that Phi Sig nationals would just abandon a chapter. As 33girl wrote, they just had different visions to improve the chapter. It is possible that is where the misunderstanding occurred.
Wow! this is long!