There are analog DVI ports, DVI-A. Although this is a spec, I've never seen one in the wild. But it does exist. You are correct in that an active adapter is only needed when going to VGA. Because there are no analog ports on the 10 series. Knowing the parts involved would help a lot.
Edit: There are three different DVI ports. DVI-A which has the four pins needed for analog video. DVI-I is what most people are familiar with. These are the ones that can use the simple adapter we all know. DVI-D is digital only and doesn't have the analog pins for the simple adapters to work.
https://en.wikipedia.org/wiki/Digital_Visual_Interface