How can I truly DELETE data from a SQL Server table - still shows up in notepad in backup file?
The problems with your approach:


if DELETE compacted the pages immediately, it will cost more I/O than it is worth. The point of RDBMS is to be fast. It will also not help fillfactors and b-tree balancing (indexes)
not mentioned, but similar - if DROPping columns really removed data immediately, it would require a large amount of I/O to completely restructure the table
DBCC Shrinkfile + NOTRUNCATE is already a brutal operation, it shuffles all used pages from the end of the file towards the front.  To have it move data within pages is even more expensive and would be a very bad idea, since you will end up with FILLFACTOR of 100%, which is very rarely a good ideal at all.
sp_clean_db_free_space which you have found is not risk-free, as Book Online clearly states. It is not something they envision sane DBAs to be running often (if even more frequently than once per lifetime), hence the warning "Before you run sp_clean_db_free_space, we recommend that you create a full database backup.", one of few procedures to carry it
If your database is full-logged, the transaction log contains a copy of the data before you removed it, so you need 2 iterations of backup before the log (contained in the backup) will no longer contain the data removed.