Can I assume that the reference to WordPress.org is because this is a generic error message, and not that you're actually running on that site?
No. I think it IS because it can't reach Wordpress.org. The plugin manager canít find it and the RSS error is for the RSS feeds on Wordpress Updates, etc. And, the backup thing can't reach dropbox.(Edit to clarify. I am NOT running on Wordpress.org but Wordpress checks WordPress.org for updates and it backs up to Dropbox; neither of which are working)
So I do think it is possibly a DNS issue but I do not think it has anything to do with white and black lists or reverse DNS.
The site itself works fine for not but I can't back up and I can't get software updates.
Note that nothing changed on my end when this started happening either