Earlier quoted context omitted.
Who's to say they can't be convinced to push a one-off update to your account/machine. Perhaps a transitory one, to help cover their tracks? The underlying problem is that you're trusting closed client software from a third-party. Once that is running on your system, arguably it's game over as far as what Dropbox or its like can and can't do to you. (If you trust them, ok. But when documents state that "they're next"…
https://grepular.com/Protecting_Your_GNU_Linux_System_from_D...
FYI this article suggests to use encfs for an encrypted folder in your dropbox, this comment https://news.ycombinator.com/item?id=5855465 suggests that this might not be a wise choice, so you might want to (re)consider that part.