It's not just about labelling, it's also about not putting everything into the same generic menu. And I completely agree with the original article that anything[1] that you can pull out of the menu entirely and turn into a top-level element, you should. But freshyill's comment was specifically about large sites, such as news sites, that have too many elements to put them all at the top level. And in the context of that, I'm saying that the hamburger menu is still the worst solution you can come up with. If you must hide things behind menus, group them in a way that makes sense, with a label that tells the user immediately what the menu will contain. If the user has to actually open the menu to find out what's in it, then you've already lost, because it means the user won't know to click on that menu when searching for a thing that happens to be in it. For a news site, if the user wants the Lifestyle section, they'll probably understand that clicking on a menu named "Sections" is likely to give them what they want (or perhaps clicking on a menu labelled "More" right next to a few of the most popular sections such as World News). What they won't figure out without guessing blindly is that a menu with an icon of 3 horizontal stripes is where they can find the sections list.
So basically, what I'm saying is that if you must use a menu, label it appropriately, and only put relevant items in that menu. If you have a bunch of things that aren't related to each other, they should be in different menus. A real hamburger menu is only appropriate for items that the vast majority of users are expected to never click on, and for which you're ok with making it hard to find for the rare user that actually does need it.
[1] Well, anything that you want users to actually click on.
So basically, what I'm saying is that if you must use a menu, label it appropriately, and only put relevant items in that menu. If you have a bunch of things that aren't related to each other, they should be in different menus. A real hamburger menu is only appropriate for items that the vast majority of users are expected to never click on, and for which you're ok with making it hard to find for the rare user that actually does need it.
[1] Well, anything that you want users to actually click on.