1) Bad generalization: "Multitaskers actually become bad at multitasking, by multitasking". Reading the referenced article, we can find out that it talks not about generic multitasking but only "media consumption multitasking".
2) Incorrect conclusions: "Students who browse Facebook and instant messaging while doing homework on average achieve lower grades in school". Really? Don't you think that students who browse FB instead of doing homework are probably bound to do worse in class not because of multitasking but because they are just not interested in learning?
3) Just complete BS. "For instance, when driving and talking in cell phone, our brain assigns a higher priority to responding to our the phone conversation than focusing on the road." Really? The referenced article doesn't even have the word "brain" in it. I would be very curious to find out the source. And BTW, you should probably never fly in an airplane if you believe this BS since pilots constantly listen and talk on the radio while flying planes and navigating in the same time.
Yes, multitasking is not a "native" human skill. You have to learn how to do it and some are better in doing it than others. Also, it is absolutely correct that context switch has a price. However, you can learn how to do it effectively. As the result, while you productivity in each individual task will be impacted, the overall results will be better. And of course, one of the skills is to learn the priorities of different tasks to make sure that cell phone conversation is secondary to driving the car.