They already do. They have Like buttons everywhere on the web.
But Facebook does have a good security track record. This random website does not. I don't trust them with any more information than needed. In this case, that is only a single anonymized token.
A script for finding vulnerable versions of PHPMailer on a server:
https://gist.github.com/cebe/d0f5631b432c520a2e6f6be8beddf11...
Finds also really old versions like 2.0.4.