Yes, with room to spare. I assume the grandparent was referring to a stud, i.e. the nominal "2x4" that is 1.5x3.5inches in cross section and 8 feet long :-) Sadly I cannot fit 4x8 sheet goods though I haven't tried very hard. I can definitely fit them if I ask nicely for a lengthwise cut, so I end up with 2' wide 8' strips. Those I can fit and close the hatch.

Ford had a terrible but well packaging rear suspension design in those cars. It was designed to not have strut towers so he gets the full width which is probably around 4ft.

No way does the length check out though. I haul lumber in a similar size car and 8ft is basically trunk to dash so there's no way he's hauling an 8ft by 4ft sheet without it conflicting with the driver's seat if not torso.

Individual boards should fit in just about anything though.