The problem with lids is in how they drip -- the water tends to condense and run down the sides, making it so there's uneven moisture in the dish. Some dutch oven lids solve this by putting little nubs all over the lid, so it drips more evenly all over the dish. With a paper lid, you don't get that large collection of steam in the air above the dish, so you don't run into those problems. You also won't get as much total evaporation, as there's less liquid-to-air surface for the liquid to evaporate from.
You could go with a just a skewed lid, but it's possible that the rice might come out less than ideal. (although, I'll one for taking shortcuts ... if I can get an 8/10 with 1/2 the effort, I'm all for it -- you just have to know how the shortcut might change things ... this one's a bit of a toss-up, because using a normal lid means there's one more thing to clean, but that's balanced by the extra trash from the parchment lid).