I wish I could say this, but it's never been entirely true. One of the reasons I love the linking of Windows user accounts to a given Microsoft Account is because, for Microsoft's own software, regardless of source of origin, the licenses end up being automatically connected with that Microsoft Account. Whether you have to do an N & P, a system drive needs to be replaced, or a whole new computer comes on the scene, it's just so much easier to create a Windows user account linked to the same Microsoft Account, and away you go with reinstalls. It does the looking to see if you already have this licensed, and, if so, there's nothing more for you to do.
Some of my clients are much better than others about having their stuff together, but whether residential or micro business, there always seems to be at least one vital piece of information missing, be it login IDs, passwords, license keys, etc., etc., etc.