[idlewords]

Levine's thing (linked in this thread) explains it well. At the start of the IPO, the issuing entity sells more than 100% of the shares, and buys the excess back later. Normally this overallotment is called the 'greenshoe' and is set up in a way that can't lose the issuer money. In Uber's case, they would have bought back the excess shares at the IPO price from some of the founders.

Here Morgan Stanley (legally) issued even more stock at the outset, so that it could buy it back when the price fell, propping up the price.

The reason that the short didn't push the price down like you say is that it already existed at the outset. Morgan Stanley didn't sell shares after trading began, it just created them out of thin air at the beginning, in the belief that the price would drop and that they would need the extra firepower. Had they been wrong, they would have lost a lot of money on buying back the stock at a higher price.