A free public showing of an altered, copyrighted work does infringe on the copyright without a profit. Personal use is not an infringement, IOW, you can view the altered copy all day in your home. You can show your friends at the office. But you can't play it on the big screen at the local play ground for the public to see.
Fine lines, yes, but profit is not the only infringement. Misrepresentation laws do kick in at a certain point.
Of course. Those are two seperate issues. You can't do that with an unaltered copy either... although in South-East Asia it is common to have movie nights where they show feature films for free at local temples and gathering places. I am sure the MPAA hasn't gone after them because they are not going to get much money suing poor farmers who can't afford to see the movie in the first place.