What the SEC needs to "go after" is naked shorting, and failing to deliver shorted shares.
When shorts can get away with this (think FNMA), then it can artificially drive the price down, as shorts can short a stock, and, if it instead goes up, they just fail to deliver the shorted shares, so there is no risk.
This has happened multiple, multiple, multiple times. And, its the cause of, a few years ago, with the gamestock debacle where something like 300 percent of its shares shorted. So, it was impossible to cover the shorts, when the stock went up.
The really only way to fix this is to enforce the naked shorting regulations and dont allow shorted shares "fail to deliver".