The problem is not with short selling per se. It is with naked short selling where a hedge fund floods the market with more shares than there are legitimate sellers.
First: The settlement isn't till three days later at best and is often by a FTD (Failure To Deliver which is an IOU which simply enters the system as if it was a real share of stock).
Secondly: and in any event, the offering of a flood of naked shorts (which are undetectable as they enter the system, drives the supply of 'sells' up and the price down. Then, of course, if the settlement occurs the missing phantom stock share can be bought for pennies on the dollar.
You might be interested viewing this quicktime speech-slide presentation here which explains this and related matters in detail.
BTW and one of the things that you may not know, is that of the side effects is for some corporations as also explained in the presentation, is there are now so many phantom shares that the overage is numerically more than some close proxy vote numerical differences.
Thank you for the link, enlightening.