No, that's a myth that has been proven to be historically inaccurate.
In order to use those adjuncts you have to process them separately from the rest of the mash, and then add it to the mash. You either have to do a cereal mash to pr-gelatinize them or you have to roll them with heat to make them flaked (the flaked corn you're referring to)...either way, besides the labor and energy involved to grow and harvest those plants, you expend labor and energy to make them usuable. You have to boil them in a cereal mash. That's another couple hours of labor and energy involved in the cost of the product. Same with making the HFCS ad rice syrup solids they use today....It still has to be processed before it makes it to the beer.
Maureen Ogle proved in Ambitious Brew, that when AH released Budweiser with it's corn and rice adjuncts in the 1860's it was the most expensive beer out there; a single bottle retailed for $1.00 (what would equal in today's Dollars for $17.00) this was quite difference when a schooner of beer usually cost a nickel.
Corn wasn't used to "save money" or "cut costs" like so many beersnobs like to think to make them feel superior to bmc drinkers. It was done because heavy beers (both english style Ales and the heavier Bavarian malty beers) were not being drunk by American consumers any more. Beer initally was seen around the world as food (some even called it liquid bread), but since America, even in the 1800's was a prosperous nation compared to the rest of the world, and americans ate meat with nearly every meal, heavy beers had fallen out of favor...
And American 6-row Barley just made for heavy, hazy beer.
Bush and other German Brewers started looking at other styles of Beers, and came upon Karl Balling and Anton Schwartz's work at the Prague Polytechnic Institute with the Brewers in Bohemia who when faced with a grain shortage started using adjuncts, which produced the pils which was light, sparkly and fruity tasting...just the thing for American tastebuds.
So the brewers brought Schwartz to America where he went to work for American Brewer Magazine writing articles and technical monographs, teaching American brewers how to use Rice and Corn...