Australia is known for being quite protective of it's native species.
So are Ecuador (Galápagos islands included), Ethiopia and Madagascar. That is why only a few of their endemics are common in captivity. However, I wouldn't classify the ownership of their animals in the same way I do with giant pandas. Is importing these creatures possible? Yes, but not feasible, as you would have to go through a LOT of paperwork (and even possibly a few thousands of dollar in fees), but the animal will still be yours in most cases.
You cannot legally import any cetaceans from Brazil either, as their presence in captivity has been
de facto banned in the country.
I believe no species belongs to the Brazilian government in a similar manner as to how giant pandas are all property of the People's Republic of China. I, however, can give you a small list of "country-locked" animals.
- Alcatrazes tree frog (
Scinax alcatraz): only found in São Paulo (zoo).
- Alcatrazes lancehead (
Bothrops alcatraz): only found at Instituto Butantan.
- Golden lancehead (
Bothrops insularis): only found in a handful of collections in São Paulo.
- Vitória island lancehead (
Bothrops otavioi): only found at Instituto Butantan.
- Franceses island lancehead (
Bothrops sazimai): only found at Instituto Butantan.
- Eastern silky anteater (
Cyclopes didactyla): only found in Itatiba.
- Buffy-tufted marmoset (Callithrix aurita): only found in a handful Brazilian collections.
- Southern muriqui (
Brachyteles arachnoides): only found in a handful of Brazilian collections.
- Kaapori capuchin (
Cebus kaapori): only found in a handful of Brazilian collections.
- Alagoas curassow (
Mitu mitu): only found in a handful Brazilian collections.
- Seven-colored tanager (
Tangara fastuosa): only found in Maragogi (EcoPark Sol & Mar), if not bred privately in Europe.