This is, unfortunately, kind of the expected reaction once the lost/escaped/released pets establish a colony. It's not here, it's in New Zealand and it's about IRN's, lories and toos but we've have the same issues in USA and it has been shown that it's not really true - although there might be something about their competiting with kakarikis...
https://www.stuff.co.nz/northland/10827 ... tive-birds