This is kind of a half-truth, and needs to be clarified. The slower you go the higher the percentage of fat is burned. That does not mean "you burn more fat if you go slow". You can hammer and burn more overall calories, and even though the percentage of fat may be lower, it will still be a higher total quantity of fat burned than by riding at a lower intensity.

As to the original question: riding slow won't hurt your overall performance, it just doesn't help it (in terms of improving aerobic or anaerobic endurance, etc.). It may help for recovery; i.e. many people claim that a slow/easy ride the day after a very hard ride helps muscles rebuild faster. So in that sense it may be seen as helping performance. The theory makes some sense; improve blood flow to the area without severely taxing any systems, etc.