The only way of updating system tables directly is to start the instance in single user mode and connect via the DAC. This is unsupported and unsafe however (the structure of them has changed since 2000 so the code you have won't work against them).
Luckily you don't need to do this though. You can use ALTER TABLE ... SWITCH to do this as a metadata only change in a safe way.
/*Create table with option off*/
SET ANSI_NULLS OFF;
CREATE TABLE dbo.YourTable (X INT)
/*Add some data*/
INSERT INTO dbo.YourTable VALUES (1),(2),(3)
/*Confirm the bit is set to 0*/
SELECT uses_ansi_nulls, *
FROM sys.tables
WHERE object_id = object_id('dbo.YourTable')
GO
BEGIN TRY
BEGIN TRANSACTION;
/*Create new table with identical structure but option on*/
SET ANSI_NULLS ON;
CREATE TABLE dbo.YourTableNew (X INT)
/*Metadata only switch*/
ALTER TABLE dbo.YourTable SWITCH TO dbo.YourTableNew;
DROP TABLE dbo.YourTable;
EXECUTE sp_rename N'dbo.YourTableNew', N'YourTable','OBJECT';
/*Confirm the bit is set to 1*/
SELECT uses_ansi_nulls, *
FROM sys.tables
WHERE object_id = object_id('dbo.YourTable')
/*Data still there!*/
SELECT *
FROM dbo.YourTable
COMMIT TRANSACTION;
END TRY
BEGIN CATCH
IF XACT_STATE() <> 0
ROLLBACK TRANSACTION;
PRINT ERROR_MESSAGE();
END CATCH;