I played ~20 story missions with three of my friends last weekend and out of those missions we had zero score in seven of them.
I´ve understood that this might be because one of us has a bad internet connection, but none of us had any lag or anything during the games. Also this problem has existed since launch date according to the forum posts.
It was really frustrating when you finally beat an advanced hardcore mission and see the zero score. It went to the point that two of my friends said that they won´t touch this game again until it is fixed.
Here you can find screenshots of the zero score missions: http://imgur.com/a/oKgDs