When you say "competitive firm" I'm not sure if you mean a firm in perfect competition or one in monopolistic competition.
If you mean perfect competition, the only way this statement is wrong is in the fact that it says that the firm sets its price. This implies that the firm has control over what price it charges. In reality the firm is a price taker and does not control its price.
If you mean monopolistic competition, then this statement is always false. In this market structure, a firm produces the *quantity* where marginal revenue = marginal cost. But the price is higher than marginal cost because the demand curve is to the right of the MR curve.