It's not your data because your browser fingerprint hypothetically coincides with somebody else's. Deleting the data would delete somebody else's data too.
You pose an interesting question actually, when is data you generate, "your data"?
If the data is only associated with a browser fingerprint then I see the argument for it not being your data; it's just data. It's like saying Google Street view has your data because they took a picture of the front of your business or your house. Does it make a difference if it's your business or your house? If you move out, is it still "your data"?
Next, if they have your friend's contacts, is it "your data"? I sync my contacts with a number of services, but I've tended to think of this as "my data", not my friend's data. Is it because I grew knowing about the white pages; so assuming phone numbers are public, a collection of phone numbers to name is my making therefore of my property? Even if it's a collection of data about my friends?
Lastly, I think we'd all agree that combining your name and your browsing info would constitute "your data". Is it because there's non-public data associated with your name? Names aren't really unique, is it because the combination of your name and your browsing info IS unique?
Also, is facebook capable of doing this? If so how?
