Note: This answer applies to the US side of the ISS
The ISS internal video cameras are simply Commercial Off The Shelf (COTS) camcorders. They interface with the video distribution system by plugging into Internal Camcorder Ports located throughout the pressurized modules. These ports communicate with Common Video Interface Units (CVIUs) which in turn communicate with Video Switching Units (VSUs).
188.8.131.52.2.4. Camera ports. The ISS has camera ports (part of the structures and mechanisms system), both internal and external, for
connecting cameras to the ISS. The internal camera ports are for
handheld commercial camcorders. The external camera ports (14 in all)
are for the ETVCG's.
International Space Station Evolution Data Book (NASA/SP-2000-6109/VOL1/REV1)
The ground has control of the CVIUs and VSUs, but no control over the COTS camcorders. If the crew does not want video to be taken, there is nothing the ground can do about it other than ask nicely.
Photo Credit: NASA