The technical discussion is getting confusing.
I had taken courses on TV servicing for interest (though never used that professionally as there is no money in consumer electronics servicing.) If you refer to any textbook, the front chapters with the basic concepts will do, there will be a block diagram on TV circuitry and on the TV broadcast signal.
On the analog TV sets. The audio and the video are embedded in the same signal - the composite video signal. The signal gets into the TV set via the antenna or the cable to the "Tuner" block where you select your channel. Then it enters the "IF Strip" block followed by the "Video Detector" block. From here the signal is split and output to the "Audio" block and the various "Video" blocks. The signals may be distorted, or missing audio or video only. But there is no way one signal will be out of synch with the other.
I haven't read up on digital TV circuitry but a quick search on the Internet turned up <
and there is a useful block diagram in page 2. It is still a single composite video signal which does not get separated into its audio and video components until the second PIF stage (cable ->Tuner -> PIF ->
etc.) and therefore both the audio and video arrive in synch and cannot be out of synch whatever happens inside the TV set.
A few select descriptions from this URL will be useful:
From my understanding of the above Sencore explanation digital TV is not true HDTV as HDTV will be wholly digitized at the broadcast end.