Whether the speculation is true or not, is there a precedent for this in your experience? How do you deal with it?
Some Chairmen, Presidents and CEO's can be pretty forceful.
At my present position its nearly viceversa, the boss being very, very interested in his safety, he would ask us after every landing that is not conducted in VMC wether this was dangerous....
But back to the q, as an air taxi pilot I had these issues regurlarly at hand, canīt really say there is a 'one does it all' solution to it. Some need forceful feedback, some need convincing that it is not just us being to lazy, some need to be reminded that we donīt wanīt to be forced into unlawful actions.
Most I have to say, have not exerted pressure. But then, some of us feel pressure just by being asked "can we land?"
What you have to have in hand though is a second solution. Like, "well, Iīm sorry, but Farnborough is closed for weather, we can get you to Luton and have a limo ready and reposition to Fab when the wx has improved to pick you up later in order not to hurt your schedule more then necessary". If you can provide a new calculation and what time penalty is involved you have done your homework correctly.
Also, when in doubt bout the wx, I tell my guests up front that we might need to divert and ask which alternate (obviously one mentions only the ones that should work) would be more convinient should the need arise...
Just standing there saying no, not poss, is definately not to the liking of most pax I flew yet...
All in all, just use common sense.