Maybe your aunt was referring to when a band would be an indication of it being captive bred, as to discourage the practice of wild caught back when exportation became illegal.
The bands are mainly used for the breeders info. for record keeping and genetics. Most breeders band, but I've bought juvenile weaned birds from bird stores without bands. Maybe because the breeders didn't need to keep track of the babies since they were going to be pets sold from the bird store?
It means nothing to a pet owner. BUT, a good breeder will give a (most likely 72 hr) health guarantee. If you take your bird to the vet during that time, and it is found to have a 'defect' or any tests come back with problems, in order for the breeder to honor the guarantee, they have to have "proof" that this bird indeed originated from them, so a band serves as ID during this period. If they don't band, then ask how they do this health guarantee (if they have one).
Also another rare circumstance where a band would be needed, for example, I used to keep a Cuban Amazon which is on US Fish and Wildlife endangered species list. If I were to move to another state and do it legally, the bird would need a permit. In order to ID the particular bird, I imagine a band would be necessary, though I wasn't going to move far away. My vet who hates bands (for safety reasons) cut it off.
Can't think of other reasons off the top of my head maybe others can. It doesn't necessarily mean bad breeder though.