Background (with a little speculation)
Inside the TV's switch mode power supply will be one or several Y capacitors that connect the internally produced DC voltages to either live or neutral. They are there to reduce the common mode noise produced by the high frequency switching transformer from affecting the DC outputs. Without the Y capacitors, all the internal DC rails will be wobbling up and down at 100 ish kHz due to inter-winding capacitive coupling between the flyback primary transformer and its various secondaries. The wobble will not be massive but could be around 1 volt p-p.
If this were not a TV, then there might be no real use for the flyback noise suppression capacitors but, consider this; the TV has to connect to an antenna of some sort and, you don't want the noisy internal 0 volts of the TV to be superimposing several volts peak-to-peak of 100 kHz onto your antenna or satellite input signal. You might be sharing the antenna system with other homes (say in an apartment building) so, the internal design of the TV has to accommodate this scenario. If using a satellite dish then it will be connected via long wires with high capacitance to ground and 100 kHz noise is going to cause some detriment somewhere to the received signal.
The infrared remote receiver in the TV will be active all the time whenever the TV is plugged into a wall socket so it will be constantly looking for an infrared signal that is encoded as "ON". The infrared detection circuit will use high gain circuits that feed into a form of data slicer that gives a digital output so, how many bits of encoding are used to represent "ON" and how long will it take random noise (via a high gain infrared detection circuit) to erroneously reproduce the bit stream that represents "ON"?
I have had some experience here to draw on. A high-speed data link I designed (650 Mbits per second) when not connected to a valid signal would trigger approximately every millisecond or so to indicate it had received a correct frame ID and, about every minute or so it would find exactly the same frame header in exactly the right place hundreds of bits later on. It would then indicate that it had received a valid frame of data. Of course it hadn't (and we knew that) but, just like false alien transmissions that people rave about, the hardware told us differently. Just random numbers coinciding.
Tossing a coin
How many times would you have to toss a coin to get 16 heads in a row? The data stream was 650 Mbps and in 1 ms the data receiver would get 650 kbits (with one false positive) - so "tossing a coin" 650,000 times resulted in a good chance of seeing 16 consecutive heads. OK I can't remember whether it was 1 millisecond or 5 milliseconds but, the point is this; if you do the experiment enough times (and very quickly) the number of false positives will be huge!
What has this got to do with the question?
If the Y capacitors were connected to the neutral incoming AC lead, it would offer better noise reduction than if it were connected to live. Now clearly, the live and neutral wires can be interchanged so you could ideally choose to have Y capacitor noise reduction capacitors connected to the "earthier" of the incoming AC wires and, if this gives slightly better noise reduction on the infrared detection circuits then it might make a big difference in receiving a false "ON" demand every hour or so and detecting a false "ON" every month or year.