This thread is of considerable interest to me as in a prior life, I was a biomed tech in a hospital and one of my duties was to see that everything metallic within the patient's reach was at iso-potential ground. Most hospital rooms now have the TVs mounted high on the wall and out of reach but harder to control are the"goodies" brought in by family members to entertain the patient.
The problem in the old days was particularly severe and often an old "hot-chassis" TV would be brought in from home and set up on a bedside table. Invariably, the polarization of the power plug was defeated if present and the rabbit ears had long since been replaced by a wire coat-hanger shoved down into the antenna hole or an air vent until it contacted the chassis. I recall an ICU patient with more "hash" than ECG signal on the monitor trace and the nurse (who had made the trouble call) could not understand why it went away when the TV was unplugged: "You can't do that...it is their only source of entertainment." Might have lead to an early discharge as well
Mahjonng's comments imply that the same problem may exist today with grounded inputs on the monitor/tv back being at 1/2 the mains potential.
Just for fun, I just put the DVM on the shield of my older ViewSonic (fluorescent back light) monitor and it had only 5-6 mv present but was connected to a grounded and operating computer and it is grounded through its mains plug. I will have to check our late model (LED back light) Samsung TV.
All the above not withstanding, I have often had the experience of an RPi rebooting when the HDMI plug is inserted.