My apologies Gimo but you have lost me. I did however pick up on...

My apologies Gimo but you have lost me. I did however pick up on your words "However, the index fund sells these shares to itself"

I didn't know you could do this but if true. it opens up endless possibilities. e.g.

I borrow a million shares. I then sell them to myself - presumably with a cross trade
There is now a million shares shorted but I still have a million shares which I can hand back at any time. The only cost to me is the brokerage, which i understand for brokers (market makers), is very small.

I then rinse and repeat many times with the result that their are now n million shares shorted but I still have my million shares - which I can still hand back to the original owner.

Is this possible? If so it makes looking at the number of short selling a pointless exrcise.