I don't really follow your reasoning unless your bosses have already shown they're malicious people. At work, my work calendar is shared with the entire company to see. I like it as it lets people easily schedule meetings with me, know at which of the two locations (or at home) I am. I have a personal calendar which I don't link to my work calendar at all. I do think that accountability is an important part of healthy work relationships with managers because (with good managers) it comes with autonomy. Why do you think your bosses will use it maliciously?
Right, but what other browser are you going to use?