We created a project for a user where he is the project lead. It is solely a project for him to track progress of objectives he's working on. He is a site admin and as mentioned he is the project lead. With all that, he could not delete an In Progress item but I could. (So when I double-clicked, one of the options was for me was Delete but he did not have that option.)
He also couldn't delete subtasks but I could. What power do I have that he doesn't? I am also a site admin but did not create that particular project.