Different individual geese are different so I can’t say that there isn’t a goose out there who defends the flock but generally it’s highly unlikely a goose will be willing to give it’s life to protecting anything besides it’s mate or goslings.
I think the misunderstanding comes from people that bought a goose as a flock guardian and didn’t bond well with it, once breeding season came they mistook it trying to attack them as a rival for the behavior of an animal that will attack anything that comes near it’s flock, which isn’t the case. Then there’s the problem of others repeating things they’ve heard like it’s fact without actually knowing wether it may be true or not.
Geese will alert you if a person comes into the yard by honking, chinese geese are more likely to do this because they tend to be spicier. Mine “Toulouse, Buffs, Romans” do not, they just hustle quietly off to hide because they aren’t used to people.
Geese are good at alerting other birds to predators but in a way you won’t notice if inside unfortunatly. Typically if geese see something alarming they will stand erect and issue a low “eh eh eh” sound. If it’s something small like a snake they’ll stand around and stare at it saying “eh eh eh” but for something larger “anything between a raccoon and a bear” they’ll run away in the opposite direction once they get a good look at it, usually they’ll run off silently so as not to alert the predator. They will scream if something attack’s them though.
A nesting female will scream if something aproacjes her nest to warn off whatever it is and alert the gander to defend her.
Something to keep in mind also. Most geese will tolerate the presence of ducks or chickens as long as they don’t invade their personal space, however some geese will kill chickens and ducks if they irritate them. Breeding season camps make them more prone to violence. Geese are wonderful and I love mine, but they are birds that can make life very difficult if you don’t bond with them. You can force a goose to bond with a chicken and duck, maybe even two birds by only getting one goose, but it isn’t ideal for the welfare of the goose, and it won’t prevent them from possibly turning aggressive against other chickens or dipucks they didn’t bond with.