It seems Google has the leverage, not Symantec.
A PR awareness campaign is out-of-band information that's separate from the web surfer actually navigating to a site. Millions of users would see a scary message similar to "This site's security certificate is not trusted!"[1].
To prevent scary security popups, which is more likely?
1) The website owners abandon Symantec and switch to a Certificate Authority not flagged by Chrome
or
2) Users get "educated" on Symantec's side of the story and manually add Symantec as a trusted root certificate. (Some can switch browsers but for many non-techies, that's a pain because they have all their bookmarks in Chrome -- and migrating them on mobile phone is not obvious.)
[1] https://www.google.com/search?q=google+chrome+this+site%27s+...