I think it was a kind thing to do. And there is nothing wrong with sharing information that is free and open to the public. Your neighbor is very odd that its not some alumni office's "business" to know that someone was dead or yours to share it. Geeze, the person died, it's hardly a secret or personal information.
It was nice of you. I know my grandmother's high school reunion committee/friends would want to know if she had passed. She goes to those things every time they come up.
I think you did the right thing in notifying her class. My mom graduated from a very small high school in South Central Illinois. We lived in Ohio. Memorial weekend every year, there is a dinner for all alums that welcomes the new graduating class. The special years then have other events that weekend as well. (the 5 year, 10 year, etc). For my mom's 50th, I got to be her date. I had a blast. I sat next to her PROM DATE. How often do you think of your mom as teenager, being excited for the prom etc. He was quite the catch too. He was a couple years older but had dropped out of school to go to war. He came back, went back to high school and was both class president and captain of the football team. I really had a great time, they came back from all over and were all so glad to see each other but missed those that were gone. My mom was very healthy, or so we thought. Not taking a single med. Late June she started not feeling well and went to doc in early August. He scheduled a heart cath for mid August and it went downhill from there. She died 6 weeks later. I found her classmate's email addresses on her computer and notified them. I know this isn't exactly the same thing but these people were glad to know. Even tough many years and miles separated them, they still cared. I think you did the right thing.
The only odd thing is telling your neighbor. Did you want recognition for it?
No, I didn't want recognition. He was telling me that she had lived there forever and asking us if we had to do a lot of work to the house when we moved in to update it.
ETA: He was asking about her/the house and it came up in natural conversation. I don't talk to that neighbor hardly at all.