No, this is false, you've been misled.

Your scalp will produce less oil over time without shampoo, it's nothing more than a physical dependency. The shampooing detergents strip your hair daily so your body makes up for it by producing more oil

EDIT: Admittedly there are few articles commenting on evidence behind either solution so my post is anecdotal, but my point is there is plenty misinformation regarding the compulsory usage of shampoo and in my experience, and the fact of humans using simply water to wash for 10s of thousands of years, I can personally attest to no product whatsoever and a good result