4745454b :
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
"DVI-A" (which is a made-up term) is a configuration of DVI which only includes the pins needed for VGA signal. It is an unofficial configuration (not part of the DVI spec which you can read
here), it is only found as a connector on DVI-VGA adapters/cables as a cost-saving measure, since it is pre-determined by the nature of the device that only the VGA pins will be needed. It doesn't actually matter whether they have a "DVI-A" or a DVI-I connector on the DVI side though, since they will just be plugged into a DVI-I port. It's just a matter of leaving off the unnecessary pins for cost saving. It has no impact on compatibility, because there are no DVI-A
ports that are dedicated to only sending VGA signals, because there is no reason to implement one when you could just have an actual VGA port.
Advising people that DVI-HDMI adapters won't work if their DVI port is analog-only is just adding unnecessary confusion. Such a situation doesn't exist. I mean, the HDMI specification defines a "Dual-Link HDMI" connector which is incompatible with standard (Single-Link) HDMI devices, but it has never been used; should we be advising people to watch out for Dual-Link HDMI ports too? They "exist" after all...
DVI-to-HDMI passive adapters will work in both directions and are compatible with all physically-existing DVI ports. That is the real world situation. The problem lies elsewhere. Perhaps the display has not been changed to the correct input.