Yes, 100% certain about it. You have provided a generalized overview of their business model, but that is not specific to the OTC Markets. The OTC is a tiny portion of their business, in fact it is often referred to as the "illiquid" marketplace. Either way this statement is accurate:
One of the primary functions of broker-dealers is to act as intermediaries for investors that are buying or selling stock. Often, to carry out that function, broker-dealers will handle such investor orders on a riskless principal basis. A riskless sale is one in which a broker-dealer, after having received an order to sell a security, sells the security as principal, at the same price, to satisfy that order. Regulations require broker-dealers to mark their proprietary riskless sell order as short if they don't own the security, even if the customer order to sell the security is long. Since broker-dealers generally don’t maintain a position, a significant number of such riskless sales are reported as short, even though the customer is selling long, and the broker-dealer intends to and will buy the shares from the long selling customer immediately after the proprietary riskless short sale takes place. Typically, the broker-dealer's position is short for considerably less than one second.