If a stock is listed on NYSE then gets shorted off exchange, does that mean that NYSE ignores that when calculating short volume?

Basically as I stated in the question,

I know stocks while being listed on one exchange can be traded on another exchange or off market.

I also know that the listing exchange provides short volume data for every security.

But does that short volume data specifically for the NYSE include trades not done on NYSE?

If providing an answer please provide evidence please.