Exactly. By default, subtasks are not actually connected to the project of their parent, but Asana just visually displays the parent’s project. This is a new feature that Asana just added a few months ago; you can read all about it here.
When you add it to a section, it actually does connect the subtask to the project.
@lpb touches on this distinction (and the fact that this new behavior can be confusing, as it was for you) here.