Purely anecdotal, but my brother has a small (illicit) still and has walked me through the process - it's fairly simple, and neither of us can figure out how these methanol poisoning cases could happen by accident.
Simply, the "heads" (which are high in methanol) come out of the still first, so it's easy to remove them.
In addition, methanol test strips are cheap and easy to use.
Discarding the heads is obviously best practices, but from discussions with serious scientifically minded distillers (ie chemists that enjoy brewing gin and artisanal vodka at home) the amount of methanol contained in the heads of your home distillation is hardly enough to harm you. In the worst cases if you consumed a significant volume it might give you a harsh headache (and this would be a truly large amount). If you were to collect the heads from several batches and drank that all in one go, you could probably make yourself sick.
Now say you're a shady corner store owner and you take some denatured alcohol or other spirits and dump it into some cheap vodka and sell it under the table as 'moonshine' or something else to make a quick buck...yeah you're going to hurt people. And not just a little. You could easily kill someone that way, or permanently damage them. But at home with your own still? You're way more likely to start a fire than you are to kill someone with your distillate. Unless you start cutting your output with other not-for-consumption spirits.
Aside from removing the heads to avoid death and blindness, it's also done for flavour and aroma - they have a nasty, "chemical/solvent" smell (and I'd assume taste).
Simply, the "heads" (which are high in methanol) come out of the still first, so it's easy to remove them.
In addition, methanol test strips are cheap and easy to use.