It is true that sometimes they require warrants. Also, Dropbox probably just wants access to my data to change my password in case I forget it. But technology can help me to avoid trusting them by encrypting everything in my end. Both the government and Dropbox employees are humans, and humans sometimes don't behave well. I'm willing to miss some features to get more privacy.
In the latter case, at least, it feels similar to your landlord letting the cops into your apartment.