Alex was a special case. He had received decades of organized schooling from scientists, who I'd like to think make better teachers than birds.
You can be sure that the birds in this article are just mimicking sounds.
Alex was not a special case, excepting that he was the first to demonstrate that what we were wrong in what we thought the limits were. Dismissing Alex because he got years of education that other birds didn't get avoids the reality of what he represents. That education produces better results in communication and thinking skills isn't really all that surprising, in humans. What Alex demonstrated was that the abilities of non-humans can reach significantly higher levels than we ever thought was possible. Dr. Pepperburg is still working with Alexs flock mates, and produces similar results from them without the "decades" of training.
This is not unlike humans, there is certainly a variation in what each individual is ultimately capable of, but if you don't know that a human is capable of math, you don't try to teach them, once know that the bar is higher then you strive for it, and, like human education, as you understand how to communicate with the student more, you can educate them faster.
The systematic approach to teaching Parrots, particularly Greys, produces faster results, I'm sure, but that doesn't mean that the birds don't teach each other, they most assuredly do.