Funny, I've never had an issue downloading the installation media using the code of an OEM sticker.
One hint, though: During the installing procedure you will be asked for the code. You can't type it wrong, there's some hidden formula that checks for errors. However, after having finished the installation you may find out that the code isn't valid for activating. If so, simply choose the "give another code" option and retype the code. That should do the trick. I've noticed this especially when doing a clean install using a brand dedicated code.