The grandparent is talking about modulation within a song. Unless they normalized each section of each song to C without saying so, modulation is still an issue. For instance (though I greatly doubt it's on their list) Jethro Tull's "The Whistler" has one key for the verse, a different one for the chorus, and yet another for the whistle solo...
Right, all of the songs were normalized to C, which exactly the point. At Hooktheory.com you can examine all of the songs in relative notation (i.e. I IV V in place of C F G) which makes it easier to compare chord progressions without having to bother with their respective keys.