Register? I do believe you mean they are required to be “MARKED” short in accordance with SEC Rule 200. That marking of “short” has nothing to do with a position or the trade itself and is purely to denote “OWNERSHIP” of the actual shares in the transaction and nothing more. That ownership can in fact sometimes be secure and verifiable to be that entity, and other times the ownership can be in question as to when it will be delivered. If ownership cannot be proven or the delivery is questionable then the SEC requires any broker or broker dealer to “MARK” the trade “SHORT” as part of riskless principle.
You can read about Riskless principle here from NASDAQ Notice 00-79:
I also suggest reading SEC Rule 200 and 203, as they outline the multiple reasons for “MARKING” trades short. In the case of a Grey market security, short volume is nothing more than shares transferred between different brokers who cannot guarantee settlement of that trade on T+3 as required by the SEC. Internal orders processed within brokers are obviously guaranteed to be settled within T+3. Due to no centralized market place within the grey market, anytime a broker goes outside of it’s own network to complete a trade they will in fact “MARK” it short for riskless principle.
Yes, believe it or not on the grey market it requires your broker to call (PHONE) out to 3 different brokers for shares if they do not have the shares for sale within their brokerage at your price. They must execute that trade to the best price per your instruction. That is why the greys are so illiquid and price execution becomes so poor over time that eventually no trades occur.
You can see large volume at times especially if the shares sold are newly issued shares, as SEC Rule 203 requires “MARKING” a trade short due to potential restrictions not being lifted in time for settlement. There are a multitude of causes for short volume and either way it has nothing to do with an actual short position nor NSS as touted.