Shorters also apply downward pressure that might not exist naturally, since they're selling borrowed stock. AFAIK they could potentially short more stock than is even issued by the company. It's understandable why some companies would be irritated by people doing that.
You are talking about naked short selling. I think except by a few vocal opponents (e.g., Overstock CEO) generally naked short selling is not considered a major concern in the market as Long as it is not abusive.