Right as far as I know. We share the same experience.
I have no idea about other birds than chickens. But chickens don’t seem to care about color or size of their ‘offspring’. Must say I never had a complete flock of the same colour
and breed.
I had all kind off eggs under my broodies. The broodies hatched larger eggs, got larger chicks, different look and getting a very different pattern a few weeks after hatch. After a few months the Amrocks got much larger in size, but the 2 broodies kept mothering their adopted eggs/chicks/juveniles.
Some people even had broodies who hatched ducks and raised them. Read it somewhere here on BYC. The hen panicked when the ducklings went into the water the first time. She waited nervously at the borderline till the ducklings got out. After this, it became a routine to follow the ducklings to the water and wait patiently until they came back on land.
I wonder what broody hens would do if they hatched reptiles

or dragons

? Hopefully they eat them before they get eaten.
PS found a video on youtube. It was on the Belgium National news 8 years ago. The man tells: “a hunter found a nest with warm eggs beside the water where a farmer just mowed. There was no mother in sight anywhere. Thought it were pheasant eggs. He asked if I had a broody to hatch them. See how she acts.