You know, I just looked at that pic again, and noticed how the top surface of that stand extends a couple inches past the legs on all four sides. You could actually construct a structural framework out of 2x4's and 2x6's cut carefully to be a snug fit between the floor and that top overhand. As long as the cuts are precise and the lengths are perfect, those four columns in the corners could indeed help the top bear the load, and could be connected to each other with horizontal members without actually being physically attached to the metal stand. This would of course need to be assembled in place, but that would make it very easy to build.
This might very well be justified if the load-carrying capacity of the stand requires that the weight be evenly spaced over the two levels; you'd need to read the specs to determine this. If that 4000 pound capacity is split evenly between the top and bottom shelves (not saying that it is, but provisos like that are not uncommon) then the aquarium on top might potentially exceed the rated capacity of just that top level...which would make a support structure a good idea.
Might be worth checking into this.