Both Ars and Quartz refer back to a phone interview done between Nick Bilton and Facebook's Sam Lessin in which Lessin said that "one-single digit percentage of users" had worked with Facebook's original ability to "hide themselves on Facebook's search." Because 1% of Facebook's users is somewhere in the tens of millions of people, the one single fantasy "hide me" button's disappearance became the main subject.
In fact, you are still able to hide yourself from Facebook search, and not just by deleting your account entirely (which is always an option, of course). What you're able to do right this minute - aside from the collection of Privacy assurances and how-to demos given by Facebook earlier this week - is to go to your Privacy Settings and Tools tab and check it out: "Who can see my stuff?" and "Who can look me up?" the both of them.
You can change "Who can see your future posts" to "Only Me", go to your Activity Log and cut out everyone on everything you've ever done, and "Limit The Audience for Old Posts on Your Timeline" with a single button - that's limited to your Friends, mind you. You can update "Who can look be up" from "Everyone" to Friends only, and you can un-check "Let other search engines link to your timeline." If you do all of these things (however inconvenient it is to do several tasks here instead of just one), your visibility will indeed be limited to those you've connected to as Friends on Facebook. Make it work!