I would not agree that they are more likely to get diseases and parasites, however they are more likely to become dinner for a predator.
It's just a choice. We kept them contained for several months after we got them, then MIL talked me into letting them out (hers free range all day) and they LOVED it. So I try to let them out at least a little everyday. I personally let mine free range because even though they have a nice coop and nice run, they enjoy hunting and pecking in the yard. They love to go under the deck where the concrete foundation from an old building is - in the summer it's their favorite "keep cool" place. And since they long ago cleaned out the grass and anything growing in their run, it's the only chance for fresh pickens, so to speak.
Having said that, we've lost several birds to neighbor dogs, and one to a raccoon or other predator. You give up security when they free range that's for sure. But my girls love it, so I try to keep an eye on them and let them have some fun.