Presumably you could just cut it off from the internet by dns filtering or setting up a vlan to only allow it to communicate to your locally hosted plex/jellyfish instance.
Yeah no, that's exactly what I mean (in context of the parent to which I've replied): streaming devices are likely capturing and phoning home screenshots of their own display output, too.
But yes, a smart TV programmed to do the same is even more unscrupulous given that it can 'spy' on everything it displays, to presumably include the input of connected devices.