In this case, one reason to use printenv is that it is an external command, and so it is clearly and unambiguously seeing (and reporting) whatever the Bourne shell would export into the environment for a real command. In this specific case, it appears that set does not report such single-command variables (whether or not they have a value, eg 'FRED=barney set | grep FRED').
(I am the author of the linked-to entry.)