Mushrooms are mainly chitin - similar to shells of seafood! They have a porous structure and will absorb the oil. I feel they get kind of slimy when cooked in oil or butter.
There are two cool techniques that you can use when cooking mushrooms to make use of their composition and get what I find is a better texture.
The first is from Adam Liaw, who has an Australian cooking show. He puts the mushrooms in a bowl in the microwave and nukes them until they are soft. You don't need to worry about the exact time because the chitin is unaffected except the pores collapse. You end up with a bowl of mushrooms in mushroom broth and then they maintain a nice texture when cooked further in oil. This is a great technique if you can use the broth in your dish.
I can't remember where the second comes from. Maybe Modernest Cuisine. It is to dry fry the mushrooms. No oil, just mushrooms in the pan. Any liquid is evaporated as it is released. You can hear it squeak as they fry. The surface of the mushrooms gets nicely browned and then the mushrooms don't absorb the oil in later stages of cooking.