Fuck no! Double fuck no!
Do people actually think that? That's beyond ignorant/naive. Data in the hands of a for profit corporation, safe? Did you read the terms of service / limitation of warranty? The short version is "fuck you and your data". It's not safe from loss at the whims of market/share holder needs/etc. It's also not safe from being compromised either by internal employees or external hackers. It's also not protected by most of the Bill of Rights (those mostly apply to government vs people not business vs people). It's easily supeoned, if the business doesn't just turn over the data on request.
Safe is encrypted on multiple devices geographically (and preferably jurisdictionally) separated.
The lowest acceptable level that can still be considered safe (a very loose definition of safe) is; a copy in plain/open formats on a device I physically control/hold(my desktop harddrive), and a copy somewhere else. Mom's house, Dropbox, yahoo mail, etc.