I recently started the quest Rings of Blood Magic from the Dawnguard expansion. One of the rings is located in Labyrinthian. From what I understand, and from what I'm finding at Labyrinthian, you can't get in unless you've started the Staff of Magnus quest.

Is this true? Is there no way for me to complete the Rings of Blood Magic quest unless I start the Staff of Magnus quest?

I'm pretty sure the location of the rings is randomized, so is this just an unlucky ring placement that Bethesda didn't consider, or am I missing something?

I know it tosses the two rings all over the damn place. I had to go to Solstheim to find the Ring of the Beast.

one of the other locations is the Katariah ship from the Dark Brotherhood end quest, it really wouldn't surprise me if it was for the mage's guild part here.

It might be in Shalidor's Maze rather than Labyrinthian proper, although if you're there I guess the marker is pointing inside?

If you reload a save before getting the quest from Sadri, the locations will be randomized again and may be somewhere better.