It's important to keep in mind that the shut-down condition is a short-run phenomenon, and the condition for a firm to stay in an industry in the long run is not the same as the shut-down condition. This is because, in the short run, a firm might produce even if producing results in an economic loss because not producing would result in an even bigger loss. (In other words, producing is beneficial if it at least brings in enough revenue to start covering the sunk fixed costs.)
It's also helpful to note that, while the shut-down condition was described here in the context of a firm in a competitive market, the logic that a firm will be willing to produce in the short run as long as the revenue from doing so covers the variable (i.e. recoverable) costs of production holds for companies in any type of market.