To lid or not to lid?
What makes it cloudy is a vigorous boil. You want to have a gentle simmer. If you put a lid, it can certainly make it boil (the temperature will be higher, as it has less heat exchange), so it's not a myth. 

You are the one who knows what temperature your pot reaches after hours with and without lid. If your temperature is so high that a lid will cause it to boil, leave without the lead. If the temperature is so low that without a lid, it might get too cold to simmer and head towards the danger zone, use the lid. Only your experience with the exact same setting on the exact same stove, the pot you are using and the amount of liquid in it can help you predict how hot it will be. 

If you are there to watch the pot and adjust it now and then, then just adjust as needed.