No, Dropbox actually holds all the keys; they can access the data if they want to.

MEGA actually doesn't have the key, except for files of which they already have an unencrypted copy (since the key is derived from it).

Dropbox has access to all your files at all times, and will honor government requests to view your data.

They used to claim that your data was inaccessible without your password, but this was always a lie.