Problem: these emails came to an email account that I have never used with PayPal. And when I went on my own and logged into my PayPal, there didn't seem to be anything amiss.
I'm thinking there might be a (very well-perpetuated) scam going on. Everyone might want to keep their eyes open, and definitely not try to login through a link embedded in an email message. It's a very convincing email, by the way; professional looking, no typos, no requests for anything.