The second sentence of the abstract.
These biologists did not seem to assume that 'we are surrounded by mindless organic automatons' at all. They just didn't know and that's why they did some research. They probably started this research because they had some conviction that (at least some) birds do have control.
As simply sitting with one of these birds will quickly convince you that they aren't just smart but have a lot of control, I'm moved to think that they simply explored the inefficiencies of mechanized training approaches.
It is valid to compare vocalisation between species. Humans have it mostly under voluntary, conscious control. We do sometimes make sounds unconsciously or involuntarily, but it's not often. It's very likely the same considerations are at play for most vertebrates as well. Dogs clearly bark, growl, whine in response to what's going on around them. As well as screaming in pain if you e.g. accidentally stand on their paws while wearing heavy boots. It's almost certainly consciously controlled, because you can tell them to be quiet! I found it quite funny when I told mine to shut up after growling and barking for a while at stuff going on outside; the odd mini-growl showed they were trying to keep a lid on it not entirely successfully!
Neurologically, the essentials of the nervous system are almost entirely the same in higher vertebrates. Some things are more elaborated in some species, but the fundamentals are pretty much identical. There's even a large amount of similarity with invertebrates like insects. Which makes sense when you consider that all animal life has a common ancestor. I would be extremely surprised if vocalisation wasn't entirely voluntary in every single vertebrate species. I'm sure there's some behavioural and learned component to it, of course, but that's rather different than whether it's voluntary or not.
The general behaviours observed in a species does not imply a lack of conscious will governing individual actions. It's certainly possible that vocalisations could be involuntary. However, given our understanding of evolutionary and developmental biology, I think that it more likely that the opposite is true. However, disproving this hypothesis definitively would be quite difficult. It's difficult enough for individuals within our own species!
That's not concious. That's affective.
> It's almost certainly consciously controlled, because you can tell them to be quiet!
It's probably conciously suppressed. Although you can't be sure that suppression isn't affective response to fear of your disapproval.
We could claim that all other human beings aren't conscious as well, and that any reactions are affective only. It's clearly not serious, but claiming the same about mammals and other higher vertebrates can't be serious either given their extremely close biological similarity. It is extremely unlikely that they aren't as entirely as aware of the world as ourselves, and it is not logical to assume there is some fundamental cognitive difference when our observations show such close similarity.
In regards to biology's approach to animal intelligence and psychology, I'm currently reading (and would recommend) "Are We Smart Enough To Know How Smart Animals Are?", which goes into this topic in detail.