Note that while a negative inference may not be drawn from the invocation of one's fifth amendment rights in a criminal case, in a civil case a negative inference can be drawn.
http://www.litigationandtrial.com/2013/04/articles/attorney/...
http://www.litigationandtrial.com/2013/04/articles/attorney/...
[edit: reading this, I'm not sure his lawyer told him to do it, quite the opposite actually]
I didn't see anything in the article suggesting that, just that Uber's lawyers said they wanted him to release the information
[edited for accuracy given child comment, thanks late2part]
Again, according to that link, if evidence is relevant to both federal and state claims, the federal rule controls. So in this case I expect the federal negative inference rule to prevail.
This feels about as productive as telling someone to not think of an elephant. Regardless of what the jury has been told, they will still see a refusal to answer a question, and they will take that into account. The only way this would be possible if the jury never heard the question nor the invocation of the fifth.
That's almost always what happens. The big exception is if the defendant opts for a bench trial.