On Server 2012, despite the user being in the Remote Desktop Users group, being explicitly added to permission to sign in remotely you get this error:
To sign in remotely you need the right to sign in through Remote Desktop Services…
This seems like a bit of a bug, but to fix this, navigate to the following GPO:
Computer Configuration -> Windows Settings -> Local Policies -> User Rights Assignment -> Allow Log on through Remote Desktop Services
Then add Remote Desktop Users and also add the user to that policy manually. A GPUpdate /force on the server should then give the right to sign in through Remote Desktop Services.