I think it originated on Reddit and it's since been parroted here in the comments on basically every smart TV thread but I have yet to see actual evidence. It seems like a trivial theory to test - disconnect from your wifi or change its password, wait for ads to suddenly reappear on the TV (evidence it got a network connection from somewhere).
Similar FUD is being spread around HDMI's Ethernet channel; a way to carry network data over an HDMI cable. I have basically never seen it in the wild on any consumer device, but even if it were, it would still require the other device to cooperate and act as a switch/router to share its connection to the TV. Yet despite that every time smart TVs and privacy comes up someone mentions this.
Similar FUD is being spread around HDMI's Ethernet channel; a way to carry network data over an HDMI cable. I have basically never seen it in the wild on any consumer device, but even if it were, it would still require the other device to cooperate and act as a switch/router to share its connection to the TV. Yet despite that every time smart TVs and privacy comes up someone mentions this.