You can sell, and you can sell short. You're only allowed to sell short on upticks and there must be borrowed shares available. Naked short selling is illegal, for good reason.
Naked short selling, in the sense of entering into a binding trade to sell shares which you do not at that time possess (either owned long or borrowed) is not per se illegal. Your broker will require that you have the required margin at the time the trade is entered, however. And on the settlement date your broker will need to deliver shares on your behalf to close out the trade, either by buying or borrowing them.
For many institutional investors, they are in fact prohibited or restricted by charter or regulation from many short selling activities.
The complaint here seems to have more to do with "fails" endangering the clearing system. However, clearing participants already have strict requirements regarding maintaining collateral to cover their positions. And as I mentioned before, fails as between a broker and its customer is a credit problem intended to be addressed by the margin requirements and the prudent self-interest of the broker.
"He that sells what isn't his'n,
Must buy it back or go to prison."