SQL Server access doesn't really have any correlation to RDP access, other than that proves the user can reach the server over the network.
I've typically seen this specific error when the user trying to connect to SQL Server using Windows authentication doesn't have a login setup or an AD group they belong to setup as a login for the SQL Server instance.
Try running this command in the database the user is trying to access to see if it returns a mapped login name and a permission path:
exec xp_logininfo N'Microsoft\DBA','all'