Parrots sitting on shoulders don't drown in water or burn in lava / Parrots shouldn't go diving

Parrots that are sitting on your shoulder while going diving won't get any damage when staying a longer time under water. Tested in gamemode 0, 1 and 2
See https://youtu.be/MZPYFPf0E6s

Shouldn't they behave the same as horses do?