This statement is incorrect because price does not equal marginal cost in all competitive industries. Price does equal marginal costs in perfect competition, but it does not equal marginal cost in monopolistic competition.
In monopolistic competition, the quantity produced is set at the point where the marginal revenue is equal to the marginal cost. However, this is not the point where the cost is found. Instead, there is a demand curve that is higher than (to the right of) the MC curve. The price is found by drawing a vertical line up to the demand curve from the MC = MR point.
In such a market, the price will not be equal to the marginal cost.