Thanks, you grizzled vet.
I reinstalled the whole shebang, and still had the same problem: Asked to reset my password, received an email message as promised, but when I followed the link in the email I get “Sorry, that key does not appear to be valid.”
If, however, I deleted all files and -then- reinstalled, it worked.
Unfortunately, that’s not a practical solution for people who don’t want to delete their entire website.
I do think this is a WP problem, as there are many queries on their support forums…