An alternate, and which I use, is 1Password which doesn't store our database of passwords and whatnot on their services as it's a local file. You can sync it with Dropbox and it's therefore on Dropbox's servers but it's secured in some way. I remember trying LastPass but dropped it because of security worries.

You're definitely right about it being amusing at what get's people in a row. The main difference between this and the phone apps is that they deliberately chose to place their data with LastPass. So, it seems to be not the content but the authority that matters.