Most sockets don't have a grounding terminal since the bulbs themselves don't have a ground. The grounding conductor is usually attached to the metal case/reflector, not the socket itself. This is to provide an extra level of safety if there were ever a short and the reflector were to become energized. The ground gives a path of lower resistance for the energy to travel through than your body would, thus reducing a life threatening shock to a slight jiggle.... ideally... may not always work out that way.
I just looked at four different mogul light fixtures to double check. All of them are grounded to the reflector, not the socket. Fixtures are a variety of ages from a 20 year old parabolic to a year old radiant V reflector.
The short little stub of aluminum wire isn't going to hurt anything. It'll have slightly higher resistance through that portion of the wire but that's about it. However I highly doubt it's actually aluminum, probably plated copper to reiterate the point that it's the neutral side.
