Earlier quoted context omitted.
I would not say so. In agile, individual developer does not have personal responsibility for anything. In this system, individual person had own task and was accountable for that task completion. It also sounds like they were working independently and wouldn't get help unless they asked for it. "I will fire you if deadline is suddenly not met and no one else is there find out before if you don't say so" is on the opp…
In agile, individual developer does not have personal responsibility for anything. Where in the world do you get this idea? For one, there is no such thing as "agile", in the sense of a prescriptive methodology that would make such a declaration. There are just individual methodologies that claim varying levels of adherence to the Agile Manifesto[1]. And even then, the popular "Agile" methodologies like Scrum, XP, et…
"Some say that teams are self-organizing and that you succeed or fail as a team"
That is opposite of personal responsibility. There is very little space for making individual decisions and being responsible for them. If you like, you can force your vision, but whole team will be responsible if it was wrong - not you. If you like, you submissively accept other peoples opinions and it will still be the same thing accountability vise.
"I think everybody understands that that later part doesn't mean you can just come in and stare at the walls all day with no consequences."
No you can not and that is good thing. However, it is totally different then case described in the article where employee had to manage own long term tasks without any supervision at all. Article implies that employee was responsible for communicating delays without anyone actively asking about it.
"If someone is "checking up on you every four hours" it's almost 100% certain that whatever process you're using has absolutely nothing to do with "agile"."
Tasks are supposed to be split into small tasks of maximum of half day length, you report on them as you go, there is daily standup and progress is supposed to be evaluated every week.