I'm pretty sure it's the games as opposed to the TV, it's the same on my other large LCD screen, and most games and Workbench are, as you say, not centered.
If you look closely at the Lemmings screenshot you can see that the 'border' is still there, it's just been manipulated. Sensi has obviously found a way around it (overscan?)
This is why I believe this was a deliberate software configuration (by AmigaDOS perhaps?) to cater for old, round screened CRT TVs.
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