This is very false! They do not need a nest box to incubate!!!!!!
Yes they do lay eggs every other day. She can incubate right away without waiting for the rest of the clutch to be made. Sometimes they will wait so the babies hatch rather close to one another, but usually like the laying date which is every other day. IF there's a will there's a way. My Cockatiels laid eggs on a saucer plate and incubated them without a nest box and brings them close to hatch date but there were too much going on so they usually crack them before hatching so I eventually broke down and got them a nest box but I didn't want babies to begin with. But they were being so mean to the other birds in the aviary that I was forced to. That way they had their privacy and leave the other birds alone. She liked to nest near by the food bowl so that was the reason why she kept cracking the eggs cause she wouldn't let anyone eat. IF not on the saucer, she lays directly on the bottom.
The poster did say she's got a pair of keets and a lovebird.
I stated explicitly that they will sometimes improvise, however eggs laid directly on a cage floor, even if attempted to be incubated, are not likely to be a successful clutch anyway... Like you said yourself, your tiels couldn't even manage on a saucer.
The point of saying she'd need a nestbox was only for if she decided to go with dummy eggs. As in, for a place to put them. Cause throwing them around the cage haphazardly or leaving them in the food dish would proooobably not be effective.