A long time ago, companies that were compiling phonebooks also thought that they could use e.g. copyright to prevent others from using that compiled data for commercial gain. They were wrong, because copyright doesn't protect "mere aggregation" of data, as courts have ruled.
In this case, LinkedIn is not arguing on the basis of copyright, so it's a different legal argument. But the essence of the case is they same - they want to have a business model around aggregating other people's data and then providing access to that data, while limiting what people who access it can do with it. They don't have a right to this business model. If technical means of restricting access don't work, or if adopting them means that they drive most of their customers away, tough luck.