Earlier quoted context omitted.
Dropbox is a US based company, is not bound by EU data protection law, the Charter of Fundamental Rights of the EU (basically the EU's Bill of Rights), and additionally the US Constitutional ban on warrentless searches does not apply to EU citizens in EU.
Constitutional rights don't apply to Dropbox at all. They are a private entity. If they want to inspect your data, they can, especially if they have disclosed this in their terms of service. That's why I would never put anything sensitive (tax returns, etc.) on dropbox without encrypting in locally first.
This is one of the reasons the EU courts have found that US law is not at all adequate for storing EU citizens data. In the EU, the Charter of Fundamental Rights ("Constitual rights") do very much apply to your dealings with a private company.