As happens more often with a Question of the Day: Good idea, but badly executed.
If you exactly follow the instructions, executing the 'alter proc' script after making the change will result in an error (because you are trying to alter a procedure that doesn't exist). And then the statements 3 and 4 will of course also return an error.
Since that option was not available, I had to second-guess what happened when the author submitted the question. The most logical explanation was that he already had a stored procedure 'rename_by_alter' when he started creting this question, so instead of altering the proc he thought he changed, he altered that other already existing proc. I then picked my answers based on that assumption, and I got it right.
1. Using sp_rename to rename a programmability item does not change its definition in sys.sql_modules. That's why Books Online recommends to use DROP / CREATE instead.
2. You can't use ALTER PROC to rename a procedure.
3. Submitters of a Question of the Day should always test their questions on an empty database before submitting their question.