I believe they are referring to the Challenger lunar launch that exploded. What they believe it came down to was a tolerance issue in the O-Rings they were using which if I remember right was a concern already placed by the engineers.
The original image has something along the lines of “I hate this system” and the smug guy in the well is saying “Ah, and yet you participate in said system!” as a gotcha. I think the purpose in this one is just carrying over the smugness with which people post the XKCD when any new possible technological standard is proposed (whether or not it has any merits)
Your point regarding the legalities of the situation wasn’t missed. I agree with you that we need rights, but the point on the other side is while they can indeed say no, they cannot compel you to come in through means other than threatening firing you. They can say no and attempt to intimidate you, but firing and retraining for most non-entry level roles is a lot of work and often not worth the time and effort compared to letting an employee have a week off.
So while it is formally a request, we as employees can present it as an ultimatum and often if you aren’t terrible at your job, the power-tripping boss will realize it is easier for them to acquiesce and let you have your vacation than it is to go through the hiring process.
I think they’re arguing that unless you make yourself easily replaceable, you don’t have to make it a negotiation. They aren’t arguing the law, they’re just talking power dynamics.