I found it surprising too, but your impression is wrong.

When you query the Foursquare API for a user, Foursquare returns the user's Facebook and Twitter names in their response (if the user has provided them to Foursquare):

https://developer.foursquare.com/docs/responses/user (see the "contact" field)

Once you have that, you just query Facebook and Twitter for their publicly available profile, photos, likes, tweets, etc.