Back in 2000, the consulting firm I worked for called me up because they found my resume on Monster. They wanted to know if there was a problem, was I looking to go elsewhere, or what. I gave them three reasons. First, I'd had my resume on Monster ever since I first learned about Monster, and in fact I think that's how they found me. Second, I sometimes get Emails or calls from friends who are looking for work. Third, this is a consulting gig, on a contract with a life expectancy, and I've been on contracts before that ended suddenly so I need to remain as mobile as possible, even though I'm not looking to leave the contract I'm working.
Even if you're happy in your current gig, with no intention of ever leaving, let me direct you to speak with any number of people I've worked with in the past who are no longer working for the company they'd been with for years or even decades. The future is a theoretical concept with no basis in reality vis-à-vis employment.
As for how to respond to your employer if they find your profile on LinkedIn, I would use the Friends and Family argument. You know people who may be looking for work and if a recruiter contacts you then you'd like to be able to connect that person with the recruiter.
Another angle you could use is that LinkedIn, in your experience, is a good determinate of the market. If recruiters are contacting you from time to time, then you know that you have a marketable skill and are of value to your current employer. If that were to end, then you might have to reassess your current skillset to determine if there is something you need to do in order to remain of value to your current employer.
Finally, and I would NOT share this with management, LinkedIn may provide you with an opportunity that you might otherwise never have found. No matter how contented you are in your current position, there are opportunities out there that you would not pass up, if they were to come your way. As such, don't shortchange yourself.