USE your_db;
GO
CREATE USER username FROM LOGIN username;
GO
GRANT SELECT ON dbo.MyViewName TO username;
GO

CREATE DATABASE unrelated_db;
GO
USE unrelated_db;
GO
CREATE TABLE dbo.foo(bar INT);
GO

USE [master];
GO
CREATE LOGIN username WITH PASSWORD='foo', CHECK_POLICY = OFF;
GO

CREATE DATABASE velojason;
GO
USE velojason;
GO
CREATE USER username FROM LOGIN username;
GO

CREATE FUNCTION dbo.checkbar()
RETURNS INT
AS
BEGIN
    RETURN
    (
      SELECT TOP (1) bar
        FROM unrelated_db.dbo.foo
        ORDER BY bar
    );
END
GO
CREATE SYNONYM dbo.foo FOR unrelated_db.dbo.foo;
GO

CREATE TABLE dbo.PaymentDetails
(
  PaymentID INT
);
GO

CREATE VIEW dbo.SomeView
AS
  SELECT
    p.PaymentID,
    x = dbo.checkbar(), -- function that pulls from other DB
    y = (SELECT bar FROM dbo.foo) -- synonym to other DB
    FROM dbo.PaymentDetails AS p;
GO
GRANT SELECT ON dbo.SomeView TO username;
GO

EXECUTE AS USER = 'username';
GO
  -- even though I don't reference any of the columns
  -- in the other DB, I am denied SELECT on the view:
SELECT PaymentID FROM dbo.SomeView;
GO
REVERT;
GO

ALTER VIEW dbo.SomeView
AS
  SELECT
    p.PaymentID
    --x = dbo.checkbar(),
    --y = (SELECT bar FROM dbo.foo)
    FROM dbo.PaymentDetails AS p;
GO

DECLARE
  @dbname   SYSNAME = N'unrelated_db',
  @viewname SYSNAME = N'dbo.SomeView';

SELECT DISTINCT
    [This object] =
    OBJECT_SCHEMA_NAME([referencing_id])
      + '.' + OBJECT_NAME([referencing_id]),
    [references this object] =
    OBJECT_SCHEMA_NAME([referenced_id])
      + '.' + OBJECT_NAME([referenced_id]),
    [and touches this database] = referenced_database_name,
    [and is a(n)] = o.type_desc,
    [if synonym, it references] = s.base_object_name
FROM sys.sql_expression_dependencies AS d
LEFT OUTER JOIN sys.objects AS o
ON o.[object_id] = d.referenced_id
LEFT OUTER JOIN sys.synonyms AS s
ON d.referenced_id = s.[object_id]
AND s.base_object_name LIKE '%[' + @dbname + ']%'
WHERE OBJECT_ID(@viewname) IN (
        referenced_id,
        referencing_id,
        (SELECT referencing_id FROM sys.sql_expression_dependencies
        WHERE referenced_database_name = @dbname)
) OR referenced_database_name = @dbname;

create login YourTpvLogin with password = 'enter new password here'
go

use SomeDb
go

create user YourTpvUser for login YourTpvLogin
go

grant select on YourView to YourTpvUser
go

execute as user = 'YourTpvUser'
go

select *
from YourView

revert
go