Is the crux of the argument that justification is an arbitrary line and ultimately insufficient?
These are correct but contrived and unrealistic, so later examples are more plausible (e.g. being misled by a mislabelled television program from a station with a strong track record of accuracy).
The point is not disproving justified true belief so much as showing the inadequacy of any one formal definition: at some point we have to elevate evidence to assumption and there's not a one-size-fits-all way to do that correctly. And, similarly to the software engineering problems, a common theme is the ways you can get bitten by looking at simple and seemingly true "slices" of a problem which don't see a complex whole.
It is worth noting that Gettier himself was cynical and dismissive of this paper, claiming he only wrote it to get tenure, and he never wrote anything else on the topic. I suspect he didn't find this stuff very interesting, though it was fashionable.