I hired a salesman for one of my businesses. He had limited sales experience but I was willing to train. His Linkedin account had maybe on or two dozen contacts. I watched as he systematically added contacts to the account over a year. Nearly all of these contacts came out of our business activities. By the end of the year he was in the hundreds of contacts. The relationship wasn't working out and I had to let him go. He went to work for a competitor. Not only was he armed with the knowledge from this one year "training program" but now he had a who's-who of the industry in his LinkedIn account. Business can really suck sometimes.
Some of these contacts were developed after non-trivial financial and monetary investments. For example, we were spending about $250K per year going to tradeshows. Some of these contacts came from relationships built over making contact with people repeated times at various tradeshows spread over several years. In some cases the tradeshow activity was followed-up by in-person visits at the customer site. One could easily argue that some of the contacts easily cost tens of thousands of dollars to develop.
Who owns these contacts and relationships? I think it is very clear that the business does. I also understand that this is not a trivial problem. These days it is nearly impossible to control the exodus of internal data, be it contacts, code or design data (electronics, mechanical). One personal Dropbox account and an employee can move hard drives worth of data out of your business. Agreements not to do so are only worth the paper they are on. In the end it might just be a matter of personal morals and ethics.