Sql-server – SSMS connects, Linked server fails

There's a SQL Server 2012 machine which I have login and password. It's a SQL Server login, not an AD one.

I'm able to login using SSMS. But when I configure a linked server in my SQL Server I get error message saying this login doesn't have access:

Cannot process the object ""DB"."SCHEMA"."TABLE"". The OLE DB provider "SQLNCLI11" for linked server "SERVER" indicates that either the object has no columns or the current user does not have permissions on that object.

Any idea why this is happening?

Update: This is the scripted creation of the linked server:

USE [master]
GO

/****** Object:  LinkedServer [REMOTE_SERVER_HOST]    Script Date: 16/03/2016 13:56:56 ******/
EXEC master.dbo.sp_addlinkedserver @server = N'REMOTE_SERVER_HOST', @srvproduct=N'SQL Server'
 /* For security reasons the linked server remote logins password is changed with ######## */
EXEC master.dbo.sp_addlinkedsrvlogin @rmtsrvname=N'REMOTE_SERVER_HOST',@useself=N'False',@locallogin=N'LOCAL_LOGIN',@rmtuser=N'REMOTE_LOGIN',@rmtpassword='########'

GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'collation compatible', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'data access', @optvalue=N'true'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'dist', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'pub', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'rpc', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'rpc out', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'sub', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'connect timeout', @optvalue=N'0'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'collation name', @optvalue=null
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'lazy schema validation', @optvalue=N'false'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'query timeout', @optvalue=N'0'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'use remote collation', @optvalue=N'true'
GO

EXEC master.dbo.sp_serveroption @server=N'REMOTE_SERVER_HOST', @optname=N'remote proc transaction promotion', @optvalue=N'true'
GO