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.
They went into the first day of trading >115% short so they could buy more in the open market. As they cover the short they are adding buying pressure, but if the stock is down from the offer price, also making a handsome profit on each share
My understanding is that these short positions were opened before the stock was listed, so they would not put any downward pressure on the market. However it did allow MS to buy more shares of Uber after open to try to support the price, without actually buying a large piece of the company. What where MS intentions, supporting the stock or profiting from an expected crash? The article has chosen a side, but delivers no evidence.
How does MS taking a short position help the stock?
My (naive) understand is that a short would add more sellers, typically driving the price down.