Where is that quote from? It is self-contradictory, and pretty much just plain wrong.
Current will flow if a load is connected between a generic power supply positive and negative, no ground connection is needed, unless you have some special purpose power supply.
A ground connection is often used for safety, especially in line non-isolated supplies, or as a means to reduce noise. Even so, not all supplies pass the ground on to the output terminals or even make it available (for common examples, think wall-warts and such with just a two pole output). Many supplies don't even have an incoming ground terminal from the mains (small switchers, and again, wall-warts).
I was going to post this as a comment, but it seemed to cover the question.
Edit as per comment below and corrected text.
Well, that does change things. Generally, a DC power supply has no output tied to ground, or connected to the supply electrically at all, so connecting a load between an output and earth ground would result in no current flow. Supplies that have an output set of terminals and a separate ground can often be configured (by jumping ground to one of the output terminals) as positive ground or negative ground if desired.
Your assumption is based on the fact that all voltages are referred to a "common" ground. But that's not true!
The voltage is also called "electric potential difference"; note the word "difference".
This means that a "3V voltage" means nothing; you should specify with respect to what. In your case a "3V voltage" battery is a battery whose + terminal has an electric potential 3V higher than its - terminal. If you try to measure the voltage between either of its terminals and the ground, without making any connections, you will always read 0V.
That's why you can put batteries in series to get a higher voltage.
Best Answer
How well this works will depend heavily on the bulk resistivity of the soil and the ground rods used at each end.
National Electrical Code Sec. 250-54, requires that the resistance to ground of a buildings ground rod must be 25 ohms or less. If you attach a similar rod at the far end of your setup then the best you can guarantee is that the return path is less than 50 ohms, but how much less you can't know for sure without measuring.
If you use this setup you are effectively putting a series resistance of several 10s of ohms in series with your load. Worst case, if the ground impedance is 50 ohms then the maximum power you can transfer to the load is (120V)^2 / 100 ohms / 2 = 72W.
From an electrical standpoint, the main downside is not being able to deliver a lot of power.
From a legal liability standpoint, it might not meet building codes, which by itself is good enough reason not to do it.
From a safety standpoint, its at least possible to have proper grounding at both ends, since you need a ground rod at the far end.
From a cost standpoint installing the extra ground rod might cost more than just buying the extra wire.