1. Birds build nests in the spring. In Australia, that is August - October. The bushfire season in Australia runs December - March, sometimes April. By that time, the nest is empty, the chicks have grown up and left.
No problem, birds not only build nests but also maintain them all summer long, and sometimes they have to rebuild them when they are destroyed.
2. In any case, why would a bird fly into burning a grass area to pick up sticks and take them to the non-burning grass area to build a nest, when there is ample supply of nesting materials in the non-burning grass area?
The article told you why, and I repeated its explanation: Birds of prey are attracted to fires because of their prey fleeing from them. That they pick up a stick to bring back is not what they came for, but if they see something that seems useful they may pick it up and bring it back - and drop it again if they decide otherwise.
3. I have observed herring gulls and blackback seagulls in my local area picking up shellfish, usually pipis or sea-oysters, on the beach and flying a short distance to the sealed parking areas and dropping them. They aren't doing this for fun, they're trying to break the shellfish open so they can eat it. Birds picking up burning sticks to start fires is not much of a stretch from what I have observed with gulls and shellfish.
Yes, it's quite a stretch from what you've observed. One thing is knowing that things crack when dropped on a hard surface. It's something that a bird could discover by accident: dropping an oyster either by accident or because it proved too hard to open with the beak and discovering that now its juicy meat is suddenly accessible. A behaviorist would love to point out the very simple stimulus-response pattern. Instant reward.
Another thing is the experience that fires are accompagnied by fleeing animals so the next time there's smoke: expect food!
But the stretch comes when the bird is supposed to know not only that
1) Fire --> food,
but also:
2) Burning stick dropped in dry grass causes fire.
3) Must see to it that this fire spreads so I can dine on roasted mice tonight.
I'll go with Occam in this case, and I do so mainly because I've observed my love birds putting straws on fire when they accidentally got too close to the gas flames of the stove, taking off with them and dropping them when they noticed. Luckily they never managed to set fire to anything else, but if they had, it wouldn't have been deliberate. They didn't know what they were doing.
I see no reason to think that the Australian birds set fire to dry grass any more intentionally than careless teenagers who cause fires by dropping cigarette butts out of car windows when driving through dry areas. (But unlike the birds, the teenagers are actually able to do deliberately and sometimes do. Teenagers know what fire is, how it's made and how it spreads.)
And
bonobos ...
PS You might also claim that squirrels deliberately
plant trees!