It works the other way around too. As a manager, when some of my employees sent me messages like: "Can we talk when you have some time?" One of my immediate fears was that they are quitting because he found another job. That happened only once, the other 300 times it was just about something they were working on and needed more information.
I don't take as much issue with this happening the other way around. It's a rare opportunity for the information asymmetry shoe to be on the other foot.
That seems to imply that your opposition to a person not being spooked is not a moral one. Please tell us more about it.