I think it is worth pointing out that 1) you have no idea what Quip does with the data once it gets past their web server 2) there is no mention of "end to end" in Quip's security document https://quip.com/ABbYAZsD8nbt
There are a number of "shadow IT" single-admin Quip instances popping up both in systems I'm aware of and those I hear about from other folks, so I'm guessing it's easy to administer. I know it works without Internet connectivity because I saw someone install it in an environment that intentionally has no access.
I've always wanted Google Docs on prem so if Quip is it, that's interesting in itself especially for the security reasons. But, Google has incredibly stringent controls around user data after a particular press-involved incident involving an SRE, so while the paranoia of possibilities is well-founded, in practice they'd need a damned good reason (like a critical failure in the product) to even look. They can, and do, walk employees for getting this stuff wrong.
So theoretically, yes (good security mind), practically, not likely.
Good lesson to learn for all of us with administrator access, too, about not even trusting inside folks. The DBIR is compelling here.
So what's the real selling point, then? Like I said it seems like a hybrid of Google Docs and Google Wave.