Not exactly. First, posts go into a trash bin, and only from the trash can they be permanently deleted. That what you were looking at? Second, the privilege is restricted to Editors, and you're one, the nearest thing in WordPress equivalent to a moderator. Most people are Authors, with fewer powers, and can't delete.

Right now WordPress lets everyone in each group have access everywhere in the system. The upcoming access control system will slice-and-dice it a lot more finely, like the old model where privileges are tailored to forums, and moderators have power over their own forums.