In terms of the personal security of your data, her appointment does nothing to jeopardize that. Either it's already been jeopardized or it will be regardless of her appointment.
Her appointment to the Board should be based on her credentials. Clearly she was seen as qualified and a worthy candidate by the current Board of Directors, so I have no issue there.
She's only a Board Member, too. It's not like she's directly handling day to day operations. Boards can take a variety of different roles, but in every case the main role is always an advisory one.
You should get rid of Dropbox if it is not offering the service that meets your needs. I'll keep on enjoying my free 26 GB of storage with my personal Dropbox account until a better option comes around.