Every Game Master you spoke to doesn’t necessarily have the level of access I do, Finraziell. They’d primarily go off of what they have in the Support Article, and they appear to have been accurate in that regard.
For clarification, by “any license” I do mean any game license on the Battle.net account, not exclusive to WoW licenses. I am checking to make sure that I have that right and will update if that is not but as I understand it, the timer will refresh by logging into any WoW license you have on the Battle.net account as well as your Hearthstone license.
As I mentioned, this is something that could be updated at some point in the future as we want to be fair to all involved. This currently works within the limitations of the systems we have.