As long as you are downloading the client side code from the server, someone just needs to make a small change to the javascript and they get access to your data.
Only if you can trust the code, and then make certain that the code does not change, is your data truly safe from the host.
Cortesi (http://corte.si) has done some interesting writing on the subject. http://corte.si/posts/security/hostproof.html
He implemented a similar service (http://cryp.sr + http://corte.si/posts/security/crypsr.html ), and also worked on creating a browser addon that would verify a webpage against a known hash (https://github.com/cortesi/apphash).
Here are a couple of HN submissions on cryp.sr which have some discussions on the "Host Proof" concept: