The problem is using the 12v outlet to power the inverter. Anyone can check their own to see if they have a problem. First read the voltage across your battery-terminals with a decent multi-meter, Then read the voltage at the 12v outlet with the same meter. Note the difference in voltage. The farther the voltage drops at the outlet, the less power for the converter to convert to 120v ac, and even more loss if the TV has a power block to convert back to around 12v dc.
The other problem here is people pushing "pure sign-wave" versus "modified sign-wave" inverters. There are good and bad MSW inverters along with good and bad PSW inverters. When using the internet check what purchasers say about the equipment they buy.
There are inverters sold over here from across the Pacific being labeled as "pure sign-wave" that are not as labeled. They cause problems same as cheap MSW inverters do. I had a 350 watt MSW (Vector) inverter that ran 3 different TV's fine for 9 years. I now have a N-Power 1000 watt MSW inverter that works just fine too.
One caveat is people with smart-phones, etc., have to be more careful and use an approved 12v, dc, charger, 120v ac, charger on shore-power, or a good brand "pure sign-wave" inverter that claims it works on all 120v ac equipment.