This is effed up. In my book, the company that you're interviewing with should never call your current employer. Call my ex-employers and references I provide all you want. But if you call my current employer, I will not work for you and I will deny ever having spoken to said other company if my boss asked me. It'd be a surefire way to make me stay at my current company (and keep interviewing in other places, because I probably do want to leave).
Heck I don't even update my LinkedIn until a year or more after I move companies. I do update it way before I might want to jump ship again, just like the "Looking for work" flag. My current employer's HR department will get no direct signal that I'm actually looking if I can avoid it. I'd go as far as not using LinkedIn functionality to apply to something. For all I know LinkedIn provides a paid for service to my current employer that notifies them, that I'm interviewing.
Heck I don't even update my LinkedIn until a year or more after I move companies. I do update it way before I might want to jump ship again, just like the "Looking for work" flag. My current employer's HR department will get no direct signal that I'm actually looking if I can avoid it. I'd go as far as not using LinkedIn functionality to apply to something. For all I know LinkedIn provides a paid for service to my current employer that notifies them, that I'm interviewing.