SU can only display things minimum 1 puixel from each other on screen. This means that if you place two faces 3/8" from each other but look at them from close enought for SU to "have enough pixels" in between, there's no problem.
Once you zoom out however and this 3/8" would occupy less screen real estate than 1 pixel, SU has problems displaying it and z-fighting begins.
A bigger resolution export surely helps and this is what probably happened here; your screen resolution must be higher than the resolution you exported the animation in. Am I guessing well?