Somehow I'm unwilling to believe that Linkedin is really an exception here. More likely they don't include all the data they have on you.
I downloaded my facebook data, and the only thing that I was surprised at is that they actually give you so much of the data they have on you. I expected them to redact most of it. Is it really reasonable to think that they don't have even more data than they let you download? They're not required by law to give it all to you, are they?