As to making people take it seriously, I don't think that's their primary motivation at all. As of yesterday, Cuomo himself admitted that there is a lot of unused ventilator capacity in NY. Meanwhile the press is reporting that they're running out of beds and ventilators, possibly causing people to freak out and leave NY, dragging disease to where it has not yet proliferated. This is extremely irresponsible.
On the other hand, your last point does reflect a real problem with the media's strategy here. Gross manipulation doesn't allow the media to effectively communicate the subtle distinction between "this is an emergency, we must act urgently or New Yorkers will think they've been hit with the plague" and "our emergency response measures are largely expected to work, it will be tragic but not the end of New York".