Both Bryce and Ken are correct so +1 to both of you. I just thought I would add a little more explanation to their answers.
First all fixtures and all metal parts must be grounded if installed after 1965. So if they are not you need to ground it. Originally the common belief was that it could be grounded by any method. Meaning you could ground it once at any location as well as use a mounting screw or any metal piece attached to the fixture, much the same way we used to use conduit as the grounding return, and it actually does ground the fixture. But there was always a question as to whether during a fault the over-current would make it back to the panel and trip the breaker.
So overtime, everyone in the industry starts to talk about intrinsically safe or assured grounding. That's when the industry began to modify their opinion and began redefining codes and manufacturers started attaching the tails or stingers to all of the equipment and material being installed. This included the mounting bracket, the fixture itself, and maybe even the lamp sockets.
To conclude, when you open up a fixture you need to determine, if the fixture grounded and safe? Then, what do I need to do to assure the ground is complete? As someone who once was a contractor and doesn't like lawsuits (trust me no money in it) I had policy to ground the crap out of everything.
Hope this helps to put a light on the subject so to speak.