I don’t know if it’s user-specific yet, but this is the easiest example case I’ve found so far:
https://twitter.com/modernmeds
This tweet shows up when I’m logged in (without any connections between my account and the modernmeds account) but doesn’t show up when I’m not logged in.
https://twitter.com/Modernmeds/status/ 613403902067798016
Sorry about breaking the link, my account is new enough that it yelled at me for trying to post more than five links because of all the links that get added if I actually link to a tweet.
As far as I can tell, there’s nothing special about that tweet.