Hi, there are three components to your question: does DB or any company for that matter have access to your files (has the encryption keys), does DB or any other company actually scan your data and how, and what do they do with that information.
DB does have the encryption keys meaning that they can peek into the files you have stored. As a case from 2015 proved (http://fortune.com/2015/12/01/dropbox-child-porn/) they do scan for offensive material, and they did go to the police with that information. Now, what is considered offensive is a very relative term and can change from place to place and from time to time. the Electronic Frontier Foundation keeps a close eye to such cases and publishes a wealth of information, if you care to take a look, I send you the 2015 report link (https://www.eff.org/document/who-has-your-back-2015-protecting-your-data-government-requests-0) plus some solid advice for protecting your privacy online, but, as a humble suggestion, just buy yourself a couple of external hard disks, or if you want to access the content out of home, you could set up a Network Attached Server to access remotely. I do believe it's worth the cost and the trouble..