If you are in the business that storytelling.io is in, you have to assume that some fraction of people are going to make mistakes. You also have to assume that most of those people will not be in the US. Al-Jazeera is in Qatar. Qatar only joined the Berne convention in the year 2000. Their attitude toward a DMCA request is pretty predictable.
Honestly, I found the article insulting, myopic and reactionary. The imprecise (and legally incorrect) usage of the word "stealing" is simply used to justify their outrage. Even though they appear to have edited their page 2 or 3 times to improve the content based on suggestions in this thread, it still has no details on how the original transaction was handled (what did the original author sell?). There is no indication that storytelling.io made any attempt to rectify the situation other than sending an incorrect legal request and then complaining on social media.
To be totally blunt, if I were thinking of using a service like theirs, I wouldn't touch them with a ten foot pole because they really appear to have absolutely no idea what they are doing on the legal front -- something which seems to be crucial to their business survival.
I hope they can figure it out. I'd start with realising that even when you are in the right, you can do the absolute wrong thing to try to correct it. This is going to happen again, so back up, take stock and ask yourself how you are going to improve your reaction next time.