I agree that knowing someone is important... but not necessarily having to meet them face-to-face. I wouldn't be an Alpha Gamma Delta today if it weren't for an alumna who made a point to contact me in order to write me a rec.
She was close with one of my mom's best friends - they were involved on Panhellenic together. When my mom's friend heard I was going to a school without DG (my mom's affiliation), but with AGD, she immediately thought of her AGD friend and put us in touch.
I spoke with her at length over the phone - telling her about my involvement and extracurricular activities, GPA, etc. She asked me to mail her a picture, and the rest is history.
Granted, she had a good deal of info from my mom's friend who's known me all my life, and I think that helped. So if you *know* someone who knows this PNM well, it's worth the time to look into her and give it a shot. I never knew what this AGD did with my info or picture - whether she sent it in recommending me or not. And these PNMs who contact you will never know that either (membership selection is private, right?).
I'm not saying you should lie to the PNM and tell her you'll send it, but if she ends up being someone you don't think would make a good addition to your organization, there's a very small chance this girl would never even know if you sent it or not.
Sorry if I'm babbling!
Just my $.02!