That is an incomplete summary. Their conclusion is that despite this larger than normal selection bias, the minimum wage appears to have no impact on unemployment. The paper's abstract, discussion, and summary all mention this as part of the central thesis - why leave it out?
I think summaries (by their nature) must leave something out. Considering the abstract mentions what you said (and that it's reasonable for me to have read the abstract), I think it was reasonable for the responder to focus their attention on the plot alone (which was the focus of my question).
The obvious starting position is that raising minimum wages has a negative effect on the number of low wage employees hired; because the money from higher wages has to come from somewhere and might not be available - leading to reduced business activity. This is also the classic economics position. With that in mind, there is going to be a bias towards publishing the 'surprising' results that there is no impact/a positive impact from minimum wages. The bias that this paper is identifying is surely a real thing, but it might potentially be a bais against, eg, poorly run studies that pick up spurious effects.
So the conclusions the paper draws w.r.t. elasticity aren't that interesting; we'd need to know why the bias exists before it is particularly useful. I'm a bit suspicious of using 'meta-analysis' at all because that just means that the faction that repeats themselves the most with low-quality research gets to pick what the elasticity is.
In theory we shouldn't need 200 studies to make a claim, we should need 1 or maybe a small suite (like, 5) of very high quality studies that intellectually honest economists struggle to rebut.
It's not an HN commenter's obligation to post everything a reader might want to see, certainly not highly technical point about the distinction between "this paper claims that evidence for an employment effect is over-reported" and "this paper claims that employment effect is approximately 0". They linked to the whole paper for the curious, and answered a particular question about it.
Also, the use of "despite" does not logically fit the contents of (my) grandparent poster and parent poster, as grandparent poster didn't claim mention employment as a possible positive effect of minimum wage, and even within context of my parent post, "beyond" is a better word choice that n "despite"
