So those giant mountains that comprise the vertexes of the cube would be pulling the oceans toward them. That works against your point. I don't know where the equilibrium between those forces sits, nor do I know how to calculate it.
During the course of the experiment they had to measure the shape of the mountain quite carefully and they had the idea to join points of similar height together with a line on the map - inventing contour lines.
An imagined sphere inside the cube holds 52% of the mass and so the remaining mass is divided among eight vertices, about 6% for each.
If you are off a ways from one of the points listed above, the sphere part (52%) will always pull towards the center. A lot of the force from the corners will be mitigated/cancelled by symmetry, and whatever is left over, again, it's only 6% maximum per corner.
Of course, this doesn't begin to account for the vectors, and it assumes that the density is uniform. But it should give us a sense of how much of the gravitational pull differs from our simplistic model.
The math is relatively easy with uniform density. Otherwise we have to start conjecturing on the density distribution, and without real-world feedback it degenerates to wondering if an infinite number of angels can dance on the head of a pin.
As soon as your test object is non-point you get tidal forces due to the field typically being nonuniform. As soon as your object is not spherically symmetric you get a field that looks nothing like that of a point mass.
I'd guess this is what the OP was recalling.
That doesn't apply to being on the face of a cube, though; that's not nearly far enough away, obviously. :)