How tight should the lid be when braising?
The advice isn't necessarily contradictory, both methods are valid depending on what you want to achieve. Running out of moisture in a braise is a bad thing, so if I'm braising something with limited moisture then a tight lid keeps the liquid from evaporating. A good example would be when I cook beef shin, I add a cup of water and a cup of wine, and that's all, so I don't want to lose any of it.

In some recipes you start off with more moisture than you need, or there are ingredients which are going add to the moisture in the pot as they cook (think peppers, zucchini, cauliflower). In these cases keeping the lid off a bit allows the excess water to evaporate, thickening up the cooking liquid.