The problem is doubly solved. First the cable company and TV station have kissed and made up so the Mrs. can see her shows over the cable. Secondly, I have the over the air TV working. The resolution of that is a long story that may aid others. Bottom line is my signal path fell below the input sensitivity of the Vizio.
I live in a valley about 30 miles (50 km) from the transmitting antennas. The transmitters are about 90 degrees apart, and I have no line of sight to the transmitter broadcasting the channels in dispute. My home has a steel roof and I knew from cell phone and FM radio results that an indoor antenna was not an option. I wasn't at all sure that I would be able to get over the air TV so I bodged up a quick experiment. I purchased a moderate gain antenna (single direction pattern), grabbed a couple of pieces of coax out of the junk box along with some barrels and ran the antenna some 50 feet (16 meters) to an outdoor location. Holding the antenna by hand I was able to receive the desired station with no artifacts of low SNR. I also got good signals from the transmitter at 90 degrees to my aiming direction, although the station likely to have used the lowest transmit power had severe artifacts, updating the image only once a second or so.
I concluded from this experiment that there was plenty of signal. The hand held location wasn't optimum, nor was it perfectly aimed. The cable pieces were a mix of RG-6 and RG-59. I figured there were significant losses in the cable, losses from aiming, and losses from the ground level.
The next step was to mount the antenna permanently and come up with a permanent route for the cable. This was intended eventually to cover three TVs in the house, although the problem cropped up before any attempt was made to split the signal. The house has coax routed to the Vizio TV location, left over from a previous owner, although the source was unclear. I traced the cable, found that it had several junctions between various kinds of coax, and the route from the antenna was closer to 100 ft (30+ meters). Hooked everything up and no signal reported by the TV.
At this point, I was disappointed, but not surprised. Even though I thought I had lots of signal margin, lots of losses in the actual connection was not surprising. So I bought a roll of RG6 and tested a direct connection from the antenna to the Vizio TV, routed across the floor. I didn't want to go to the work of fishing the coax through a lot of walls and finished ceilings without knowing that cable losses were low enough.
I was really disappointed to find no signal reported. As a check I ran the test cable over to another TV, which collected all signals from both transmitters over the longer cable length. I concluded something was wrong with the Vizio.
I was still stalling over diving into that big piece of gear when the cable came back and took the urgency down. Other projects beckoned. But as time became available I decided to at least wire up the other two TVs (and the Vizio while I was at it, so that it would be ready whenever I got around to fixing it). Since I would be doing a three way split, and since there was at least some evidence that my signal margin was not as large as I would like I put a gain block in. In the course of doing this I found that distribution amplifiers, which used to be cheap and ubiquitous at all hardware stores and big home improvement stores and stores like Best Buy, are no longer stocked at retail outlets and have gone way up in price in on line sources. Happened to find one on a remainders shelf at one of the local stores.
When hooked up with the added gain block, the Vizio worked.
So after all of that I conclude that the Vizio has a very pedestrian RF sensitivity, significantly lower than the other two TVs and that I got very lucky in my initial test to exceed its input threshold. I never damaged it, it just wasn't ever very good.