To your point though, and to press it further - if companies require that you exercise your options in a window after they vest or they expire - they were never really options to begin with. In essence, the vesting schedule on expiring options is a timeline for you forking over risk-filled cash or forfeit part of your "compensation."

The advice seems to suggest if their options expire if you don't buy them at a certain point (except for leaving the company, which makes sense), say no and ask for cash. If they can't pay, now you know where you really stand.