Alas, no. Bourne shell syntax allows for double quotes with variable interpolation and some other fancy syntax (including backslash escaping of literal double-quote characters), and a single-quote syntax for "raw" strings with no fancy syntax INCLUDING backslash escaping.
So your rule won't work. You can't single-quote a string that itself contains single quotes, which makes for some fun when you have arbitrary strings (file names are the big frustration) that need to be substituted into a parseable command line.
But like I said above: Bourne syntax[1] is only one kind of insanity, which is still much better than the DOS/Windows world of a separate parser for every app.
Their rule does work. The single quotes are transformed into '\''.
The first ' closes the current single quotes string. The \' adds a single quote character outside a quoted string (and outside single quotes you can use backslash escapes). Finally, the last ' reopens the single quoted string that we closed before.