Can't I just grease the Baking Sheet instead of using Parchment Paper Recipes such as http://paleoleap.com/avocado-banana-chocolate-cookies/ say to line baking sheet with parchment paper. Why can't we just grease the baking sheet?
Usually you can - our great-grandmothers didn't have parchment paper.

There are a few cases where parchment is preferrable, usually with very, very sticky dough. It saves time when it comes to scrubbing the cookie sheet.