Facebook access to WP data


I was meeting with a client today and recommending that we use the Ultimate Facebook plugin to give users the ability to log in with Facebook. They're keen on this idea, but asked a question to which I did not know the answer:

"What access does Facebook have to user's data on their site when Ultimate Facebook is used?"

I don't think that this plugin accesses any user info in the WP site. But it would be good to have some clarification. The reason my clients want to know this, is that they are an arts organisation that work with young people aged 6-25 years old, and they want to have an answer for parents, should they be asked.

Any clarification of the interaction between FB and WP for user logins etc would be helpful. I will be running WP 3.3.x and BP 1.5 for this project.