Almost everything you just said is incorrect. You don't even enter your dropbox password into the app unless you're storing it as a credential, they present a

Almost everything you just said is incorrect. You don't even enter your dropbox password into the app unless you're storing it as a credential, they present an authentication dialogue for the dropbox API just like all other third-party apps accessing Dropbox and store the OAuth key on the client. Not the server. That's why you have to re-authenticate with dropbox on every device you want to set up 1Password sync.