Only when a product's demand is perfectly elastic can one say, "If I'm producing on the elastic portion of demand, then I know that I'm maximizing profits because I'm creating where MR = MC."
In other words, the statement is only accurate if the demand curve has a slope of and the demand quantity is completely unaffected by price changes. In other words, regardless of price, buyers will always purchase a fixed amount of the goods since the demand curve is absolutely vertical.