SQL 2012 :: Closing A Security Hole

I have a purchased product that has a DB with several thousand tables in dbo. I can't change anything with the default dbo schema other than security. I have a table called dbo.ACCOUNT. It has information from multiple sites on it. I have a reporting team that need only access the information for SITE 1 on the ACCOUNT table and anything in the other 1000+ tables in the dbo schema.

I created a role (Analytics) and granted select access to dbo. I created a schema (Analytics) and assigned it the role. I created a view in the new schema called Analytics.ACCOUNT with a WHERE SITE = 1 clause on it. If they use the view, they see only the things they should. My problem is they can still do a select * from dbo.ACCOUNT and see everything they shouldn't see. How can I close that hole? I am not seeing a solution. If there is no way to fix this with roles/schemas/views, what else can I do?

Some of my pain points. I have this issue with about 30 tables. Creating custom table(s) to isolate data for each site will cost me another 2T of storage. Loading those custom tables every day would be cumbersome. Keeping the DDL in sync with the source table would be cumbersome. With the way I have it set up now, if I deny access to the source tables the view breaks because it needs access to the source tables to dynamically build the view. Here is the code I ran to create everything.

USE[DB]
--create test user login
CREATE LOGIN [Analytics_ETL] WITH PASSWORD=N'XXXXXXXXXXX'
GO
--create user in test database
CREATE USER [Analytics_ETL] FOR LOGIN [Analytics_ETL] WITH DEFAULT_SCHEMA=[Analytics]

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