Did people attempt to repair their television sets themselves back in the day and die from it?

I knew how to remove, test and replace burned out tubes when I was a kid (~12 years old). I opened our TVs, removed tubes, and replaced them myself many times. It's not as dangerous as you think. Although there were capacitors, you would have to touch their terminals or something directly connected to their terminals in order to be shocked, and those things were typically well insulated and protected. The metal chassis and almost all wiring was perfectly safe as long as you unplugged the TV.

Since virtually all hardware stores in that era had self-serve tube testers and sold replacement tubes, it's obvious that it was common for consumers to do this. It was, in fact, routine for the average homeowner.

I've never heard of anyone being killed repairing a TV, or even shocked for that matter. Even in the 1950s, 60s and 70s, manufacturers would have been well aware that building a TV with lethal voltage that could easily be accidentally contacted in a device that consumers regularly serviced themselves would create liability and very bad product PR. And above all, it would also preclude receiving a UL certification in the US, or the comparable certification in other countries. No independent safety certification and you won't be selling your consumer device in any 1st world country.

I think you vastly overestimate the hazards of older TVs.

I was a kid in the 1950s. TV sets were unreliable then, and often the problem was that a tube had burned out. My father would open the back and pick out some likely looking tubes. Then we'd go to the store. It had a tube tester with many different connector types. My father would plug the tubes in, one by one, and the tester would show the tube's health on a dial coded with green/yellow/red. If one or more tubes were bad, he would buy replacements. Then back home, replace the tubes, and try again.

My father was a chemist and savvy technically. He never got a shock.

The procedure to make a set safe for repairs is quite simple, if you know what you're doing. The danger, once the set is switched off and unplugged, is capacitors (formerly known as condensers), that will still be charged to high voltages.

The way to make the set safe is to discharge those capacitors, by shorting or grounding their contacts. Do not try this yourself. This is not enough information to do the job correctly. A trained repairer would be able to identify the capacitors, even if they weren't familiar with the model of TV and would have leads and tools to do the discharging.

Someone who'd decided to open up a set without any electronics knowledge would be faced with a set of components whose functions weren't obvious. If they started pulling parts out, they might well get a shock, but this probably wouldn't be fatal. Since they're getting the shock from a discharging capacitor, it won't last long. If they went in with both hands, they might get a shock between the hands, and hence across the heart, which could kill them, especially if their heart wasn't in good shape.

If they'd gone in while the set was plugged into mains power, they could get a mains-voltage shock that lasted, but just about everyone knew mains electricity had to be treated with respect by the time TV sets became common. If they went in while the set was switched on, then they're at risk of a long-lasting high-voltage shock, and that is seriously dangerous.

While it's impossible to say nobody got killed doing this, I doubt many deaths happened. I remember old TV sets in the UK having "Danger: High Voltage" or similar warnings on the back. Spreading legends of people getting killed tinkering with TVs would actually have been a good idea.

Sources: Basic electronics knowledge from physics classes and a father who tinkered with electronics but had far more sense than to monkey with TVs.