The off roads don’t have painted flares so I can’t say if the paint would get messed up due to them not having paint to mess up. @Bogunn has the sport, painted flares, and the OEM mud flaps maybe he could tell you if the flaps would screw them up when bent back.
It definitely could with a hard enough hit I imagine.( I don’t wanna find out!). It would have to be at the right angle though. You’d be more likely to pull the three screws out and scratch up the flare a little.