One star is the lowest possible rating. It implies that some essential feature of the product does not work at all. Parent did not say the headphones didn't work, just that they "sucked", which I can only take to mean that they did work, just not to parent's satisfaction.
> [...] which I can only take to mean that they did work, just not to parent's satisfaction.
I think you're succumbing to a moderation fallacy. It's simply not true that things must have some positive aspects to offset their negative aspects, or to use that belief to somehow interpret "sucked" as that they worked well enough to deserve better than the lowest rating (which may have increased after the replacements arrived, all we know is that the rating remained less than 5 stars.)
You can't consider having an extreme opinion on something as prima facie evidence of bias without distorting your perception of the world.
> "One star is the lowest possible rating. It implies that some essential feature of the product does not work at all."
Perhaps part of the problem is that there isn't actually any standard for what these stars mean, and what they seem to imply to you is not necessarily what they imply to other people.
To me a one-star review means "I regret purchasing this and I believe many other people will too, and consequently I want to minimize the number of other people who buy it." That regret might be the result of some 'essential feature not working' or it might very well not be. A product that works but is very low quality for the price will get a 1-star review from me because I don't want other people to get ripped off.