Thanks for the feedback. For what it's worth, we did try a bunch of alternative wordings, and Zero Knowledge was the phrase that non technologists found most accessible.
We prioritized making the explanation clear to non-experts vs. to the community of cryptographers.
That's actually not bad. I was fine with SpiderOak going for a term that is simple, catchy, and easy to market. Zero Access is the kind of alternative that might work. That specific one might have a problem: send perception of user having zero access to their own data when most clouds constantly reinforce "access from anywhere any time."
You're thinking along the right lines. I think variations of the words safe and vault have worked for other companies, too, given people understand what they do. "Your data is in a locked vault that we hold for you while you keep the keys or combination." That sort of thing.
We prioritized making the explanation clear to non-experts vs. to the community of cryptographers.