An official statement would run afoul of the law, yes. A concerted effort to whisper to many people in an effort to manipulate the market would be fairly easy for the SEC to uncover in an investigation.

A single false statement or two, said to a reporter as a confidential source, would be much more difficult to prosecute. The reporter might not willingly give up their source, and the company could deny everything, fire the person who "inaccurately represented our position", and claim the party acted of their own volition. Modest fine, at best.