I know that in a 3x3x3 this should never happen (unsolvable state), but is the same true in a 4x4x4?

(the rest of the cube is solved)

The following answer seems to say that everything about the 3x3x3 is true about NxNxN, except that the orientation isn’t fixed.

Why is a single-corner twist not a valid position on a Rubik's cube?

Does that mean that my orientation is wrong?

The cube came solved, and since this isn’t a speed cube, I don’t see how I could have accidentally twisted a corner.