Proven fact, yes.
Ask any electrical engineer, and they'll be glad to give you too much information. I should know, since I'm an Electrical Designer (not an engineer), and work with this stuff all the time, for many, many years.
If you don't believe the concept, connect a good voltmeter to a solid cold water ground (ie: water heater), and touch it to a neutral of an outlet that is running a heavy load (ie: wash machine). Use common sense when you do it. You'll get 120vac to earth ground, even though the neutral and ground are connected at the breaker panel.
The difference in resistance (only 1-2 ohms) will make the voltage choose the path of least resistance.
If you test it for current (Amps) you'll be surprised that most of the current flows directly to ground, not back to the panel. That can be 10-12 amps for a wash machine.
Don't attempt any of this if you don't know what you're doing. Less than an amp can stop the heart.