I understand that cover works by the attacker deciding on a corner of their square and checking if a line to any of the defenders squares hits something that gives cover.
But if the attacker is on one side of a doorway, and the defender is on the other side and a few squares away (away being to the side of the doorway), two of the attackers lines do not hit anything (the front two corners in the doorway). However the back two do.
Is this rule intentionally vague? Why not say "if any line" rather than "choose a line"?
Diagram. The PCs two corners in the doorway do not trace a line into any of the Goblins squares. But the top left corner does.