Indeed, I believe you are correct.

Hm. All the speaker-to-line converters I can find are for car audio, meaning it would (a) need a 12v power supply back behind the TV and (b) might not be sized correctly for the speaker impedance (though I don't know the impedance of those tiny TV speakers actually). Still, I want to try and figure out something.

Maybe something like this would work: https://electronics.stackexchange.com/a/443022

I've seen other places on the internet where people described using a simple voltage divider like that, and were unhappy with the results (noisy, etc.). Still, wouldn't hurt to try.