The use of 机 here is similar to 相机 (xiàngjī) “an opportune moment”, as you say.
The broader lesson is that Chinese characters cannot be studied in isolation, but hey, most readers aren’t here to discuss the finer points of Mandarin.
Ironically, judging from the top highlight of your story, Reid (the 4th paragraph), most of your readers seized on that catchy misinterpretation and are happy to run with it, not realizing that it’s incorrect. Oh well.
Also — amazing cover animation — was that custom made for this story??
ps: looks like Focus Blue wants us to speak ‘Murican anyhow … 😉