Stanford Alum here as well. Have answered and is the Stanford a Fund - usually current Stanford Students. I did the same thing w other dorm mates back in the 80's when I was there. Called and re verified, and said I'd donate but would not give over the phone, but asked the student to send me the info and my donation amount and received it a few days later. They won't leave messages though. It's legit.
I just got a call, 7:45 pm in the middle of dinner. I've been getting these a lot, and always at bad times.
I think it may be a phishing scam by someone who got a hold of a bunch of Stanford alum phone numbers. I'd say watch out, especially since they don't leave a message. That's always "phishy".