No, it doesn't. Imagine there is 1 share, owned by A. He lends it to B. B now (short) sells it to C. Now from C's point of view, he owns a share. So he lends it to someone. That person then short sells it.
So you have 1 share, that's shorted twice. But it's impossible for A and C to both have their loan repaid, because there's only 1 physical share.
Doesn't it unwind by just reversing the process? D buys the stock back from E and returns it to C. Then B buys the stock back from C and gives it to A.
That all sounds perfectly ordinary, as long as it doesn't happen on a deadline. If you tell D or B that they have to buy that stock right now at any price, they're going to take it in the (ahem) shorts. But if they were permitted to take their time, they'd buy it up at the market price, which would on average be pretty near the price they sold it.
It just so happens that there is a mechanism by which they can be forced to buy that stock right now, which is when F decides just on a whim to pay 100x the market price, and protection measures kick in. That's a screw-up on the part of B and D; they got sloppy and deserve to get raked over the coals for it. Everybody who wants to play that game needs to be aware of that scenario, and now they are.
But I don't think it's because there's anything impossible about having more shorts than stocks. It just takes an already risky thing and makes it super subject to manipulation.
So you have 1 share, that's shorted twice. But it's impossible for A and C to both have their loan repaid, because there's only 1 physical share.