"Oh, you can't pay for your food, you work for the restaurant now till you're paid off!"

...

but I think even by the 60's this scenario would be bizarre if it actually happened.

I did it as recently as 1994... Little bit different situation, I let them know in advance I had no money, but was willing to work for a meal, I didn't surprise them by ordering first then telling them when I was done... But they did have me eat first before putting me to work. I think that was to see how serious I was- feed me first, then if I'm a bum, they're only out one meal, but if I'm still willing once I've eaten, I'm probably worth trusting with a few basic tasks. It worked out, I ended up staying there a couple days (slept on a couch in their lounge, it was a truck stop so they had showers too) and in addition to a few meals, $50 cash.

What you say is mostly true about big chains like Denny's, or anywhere near a city, but most rural mom & pop places would at least consider it.