We downloaded PostgreSQL 9.3.5 from my.esri.com and installed it on a Windows 2008 R2 Server. Everything went fine and we were able to create an enterprise geodatabase using the Create Enterprise Geodatabase tool, connect to it, load some data, post and reconcile, all that good stuff.
We went to create some database users using the Create Database User tool and found the OS Authentication method to be disabled. We assume that's because there's probably some additional configuration work that we need to do on the database in order to enable that. We found a Postgres wikin article (Configuring for single sign-on using SSPI on Windows - PostgreSQL wiki)as well as a super unhelpful Esri KB (38151 - Configure operating system authentication with PostgreSQL for non-production servers )but they quite confusing. We then called Esri Technical Support and as usual, they were absolutely useless.