Comment by tzs
The problem with that is if someone gets a hold of the logs from both the centralized service and the social media site they can compare timestamps and may be able to match them up.
Most people will be doing the whole process (site gives token, person gets token signed, person returns token) as quickly as possible which limits the candidates for a match. Worse, if the central service is compromised and wants to make it easier for log matching to identify people they could purposefully introduce delays which would make it easier to distinguish people.
Most people will use the same IP address through the verification process which would really make it easy.
Yes, timestamp comparison will be possible. I don't think there is a reasonable way around it? And authentication on to someone else is also unavoidable with reasonable privacy. I think a system with both of those drawbacks is still preferable to most other options.