From page 250 and 251 of the DMG:
To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker's space... trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover...
It looks like they just chose the wrong corner. If the attacker was moved one square to the north it would be 3/4 cover. Or do you think they meant "choose the closest corner"?