I guess it's just a matter of getting used to, for most people who're worried about privacy. There are millions who take their web based email accounts on yahoo, gmail and the like for granted. They send personal photos, personal emails, documents and all kinds of stuff you'd be scared to expose to the external world. Corporates may not encourage this unless they can create specific contracts and agreements with web based office suite providers. But for personal use, a little common sense in what kind of information is entered would help make web based office suites a very useful tool for sharing stuff.
Sharing, collaborating and accessibility from almost anywhere in the world are the advantages for such systems - in our networked world, these outweigh any other disadvantages.