I have plenty of cover in my tank, and yet my reds are not skittish at all!
IMHO, the key is to have them get used to people around: place the tank in a high traffic area, and spend lots of time in front of your tank. Piranha's are very curious and inquisitive, and sooner or later they want to check you out from a closer range. You can also raise to water temp (about 82 degrees) to make them a bit more active and agressive, dimm the tank lights (p's don't like bright light, and actually, it's not very good to them either). I also heard that feeding p's live foods makes them bolder, but I cannot substantiate that... And the more p's there are in the shoal, the more secure they'll feel and the less skittish they will be.
I'm not saying that removing all tank decor will not help, but to me it's more like forcing them to become less shy, instead of letting them get used to their surroundings and humans at their own pace (with a minimum of stress). If they have enough places to hide, they will feel more comfortable, and will eventually show up and swim around freely more and more. The presence of hiding places gives them the opportunity to hide when they feel it's necessary (and a sense of security), and eventually they'll hide less and less.