I'd be a bit worried about the paintwork but then again, being exposed to bushes, tree sap, air contaminants and any scrotes that happen to pass by is just as bad. A breathable, UV-resistant cover should be ok and hopefully reduces the risk of damaging the finish.
On the "jealous people" point, well...having a smart car sometimes attracts the wrong attention. Having something under a cover probably attracts the wrong attention too, out of malign curiosity if nothing else. It's probably risk neutral, in that if some git wants to have a go at your car, they'll do it whether it's covered or not.