How the signal cable grounding is done in typical AV equipments
Grounding of case
The equipments which have metal case have typically grounded power connectors. In this case the metal enclosure is grounded to the ground of mains input.
There are some equipments with metal cases and power connector which is not grounded. In those cases the the metal case is "floating" (not connected to ground). This arrangement is possible and safe if everything inside the equipment is double insulated. Most modern Hifi equipments belong to this category.
Grounding of audio connectors
The unbalanced audio inputs and outputs have theur ground side of the connector wire to audio ground, which is typically connected to metal case of the equipment (because the connector are typically mounted on metal case without isolation between case and connector). In those cases the audio ground gets connected to mains input ground if the equipment has a grounded power connector in it. This is the "de facto industry standard" to do the signal wire grounding and you have to live with it.
If the connectors are balanced, then the connector grounds are typically connected to equipment central grounding point which is connected to mains ground (professional audio equipments are typically grounded).
Video inputs are unbalanced connectors. Their ground is typically connected to equipment metal case and video circuitry ground of the equipment. If the equipment has a grounded power connector, then those video inputs get grounded to mains ground.
The most commonly in recievers and VCRs then ground of the antenna input is connected to equipment metal case. This means that if an ungrounded equipment is connecte to grounded antenna network the equipment gets grounded through the antenna cable.