This cleared up that question for me. Noether showed that every physical symmetry implies a conservation law and vice versa, the symmetry of time flow and the conservation of energy are one such pair. Due to the fact that time is not flowing uniformly (Relativity) energy is not conserved.
The converse of Noether's theorem does not turn out to be true in general. Noether showed that if there is a symmetry in the system then there is a corresponding conservation law. But the existence of a conserved quantity does not (in general) imply the existence of some symmetry in the physical system.
(I should note that there are more careful ways to get something that looks like the converse of Noether's theorem, but the literature is fairly complicated -- you have to distinguish between trivial conservation laws and non-trivial conservation laws. Here's one answer online: http://physics.stackexchange.com/questions/24596/is-the-conv...)
