I don't think the Fisher 400 receiver needs to be grounded, as the design uses a floating ground. The Owner's Manual states that if you get audible hum, through the phono preamp or other inputs, then you should reverse the plug in the wall receptacle or power strip. This will usually reduce the hum.
There is nothing in the manual about connecting the ground wire from your turntable to the chassis of the Fisher. While there is no labeled grounding post on the chassis, I believe you can attach the turntable ground wire to one of the side or rear chassis screws if you find you are getting a hum without attaching this wire to a ground. But just to be sure, I suggest you ask Tuberoller, as he has alot of experience with the vintage Fisher gear, including the 400 receiver about issues associated with grounding this type of equipment.
It is however, important to make sure that the receiver has been properly maintained over the years. Most importantly, that means replacing the aging selenium bridge rectifier (usually a 2 inch square widget labeled Siemens mounted to the rear right side panel of the chassis) with a modern solid state rectifier.
Another simple but effective safety mod involves soldering a set of four resistors into the power tube circuitry to act as fuses in the event of one of the 7868 power tubes shorting internally. Much better to pop a 50 cent resistor than to watch the whole chassis, transformers and all, go up in smoke.
If you are really worried about getting a shocked or cooked through the headphone output, I suppose you could wire a fuse into your headphone cable.
One of the things I like about equipment of this vintage is that manufacturers could assume a certain level of knowledge and common sense on the part of the consumer. No need for a warning label on the chassis of the dangers of the high voltages lurking inside. Somehow people knew that the insides of radios, stereos, and televisions were not something to start poking your fingers into unless you wanted to get a nasty shock or worse.
Fortunately, a Fisher 400 receiver is too large and heavy to encourage much placement experimentation. This is one amp that is definitely not for listening poolside through headphones, or while relaxing in a bath tub.