Yes, they do. Most users, even young kids, are freaking out when you tell them anybody at Facebook (or Microsoft, or Google, or whatever, or whomever they delegate access to, can be school superintendent, boss, sysadmin, etc) can access their data. They either don't know about it, or knew about it once but decided it wasn't "right" enough to keep in mind and ignored it since.
Most users DO care and are concerned but they are so convinced there are no possible alternatives they convinced themselves no matter how terrible it is, there is just nothing they can do about it.
Please ask around, take a random person, close or not, stranger or not, technical or not, and ask them (explain if you most) if they do have such concerns. I bet they do. If they don't I'll apologize for my naivety.