They would call her (and/or other NGO) and say “we just dropped x people in the sea at these coordinated, bye!”. She would go and pick them up (she would not make any money out of this).

The crucial part about that: Captains at sea are required by law to save people or assist vessels that are about to capsize. If she ignored such a call (as the Italian government tells her to), she’d commit a crime. She’d also be liable and could be sued by the survivors or the relatives of the deceased.

She literally did what the law forces her to do, and what the Italian coast guard should be doing but isn’t.