Pressure from customers,
That might be the bigger issue than pressure from company. Especially if you have patient on board. How easy is to cancel the flight when you already made decision to go. In these cases pilots need all possible support to make right decisions. That support should be come from company, customer, doctors, etc. Not only company. This needs operational procedures and experience. Those pilots, who already have experience, need to share this atmosphere for all.
Weather sources might be somewhere incomplete. In those areas pilots needs to put more time to be sure where they are planning to go. Also might be good idea think kind of "backup" plan, if it is more lousy than expect. World most difficult maneuver with EMS helicopter - 180 degrees turn back or even land as soon it is safe.
This all should be written in company's procedures, like I believe they are some kind of way. Problem is how to handle this.