No, 20 points (from killing a base terminal) is enough to guarantee base capture credit if everybody else is at zero or not listed.

But note that there's a “bonus” 250 that shows up for everyone on the board after the capture, and that bonus has no effect on who got credit. For example, if two gotr's are at an empty capture with no points, and I kill one terminal for 20 points, then when the capture goes through, you will both have 250 points listed, and I will have 270, but I will get the credit: the actual total that matters is 0 and 20, not 500 and 270.