My company wants to control my LinkedIn profile! Does it have the right?

Q: “I have a LinkedIn profile and I just received this message from one of my bosses: ‘Hello colleagues, you are receiving this email because you have a profile on LinkedIn that requires your attention. You have left your profile in the default mode, signifying you are open to receiving career opportunities, consulting offers, new ventures and/or job inquiries. If you do not uncheck these items, we will assume that you are turning in your two-week notice and are looking for a new job opportunity ... Also, if you have not listed your current employer as (Company Name Here) exactly as such, please do so.’ Is this legal, and do I have to comply?" – Concerned, Idaho