A perfectly acceptable solution given the wording of the problem. This may be why mathematicians do not make good lawyers, and no lawyers understand mathematicians, but I digress.

Here is a reworded version of the problem.

Make a drawing connecting three houses to three utilities (water, gas, and electricity) without connecting each of the houses to each other, each of the utilities to each other, and without making one connection cross the other in any way shape or form. Each of the houses is connected to the same utility building; that is, every house gets water, gas, and electricity, from the same company and the same building.

Let's imagine that each of the utility companies reserves all airspace directly above and all ground directly below each of its lines for its own use for this puzzle, and won't let any of the others use it.