So far, I have yet to be charged for internet.
I stayed at the Memphis Marriott this past weekend. They not did not charge me. In fact, when I tried to access the internet, their I-Net Access splash page came up and it had a special note letting me know that Golds/Plats can choose any of the internet options (including the fast internet access) without any charges. And none showed up on my bill.
I suspect that some hotels are just a little slower at getting the free internet access correctly setup in their system. I might suggest that when you check-in you ask about the internet access and how you should handle it so that you won't have to spend time at check-out getting your folio cleaned-up.
As far as you doing something wrong, I'm not sure there is anything you are supposed to be doing. I haven't mentioned anything when checking-in or done anything special to remind the hotel staff that I shouldn't be charged. Hopefully as time goes on, the number of hotels that are "mistakenly" still charnging Gold/Plats will get smaller and smaller.