I found this question answer section on Parrot Chronicles:
Some eucalyptus is okay ..
I was surprised to see eucalyptus listed as a toxic plant. Many exotics live and thrive in various types of eucalyptus. Please research this plant as you will find there are over five hundred varieties and of those 11 are edible. Cockatoos, cockatiels, and budgies live in them. Many South American species also live in eucalyptus and do very well.
--Melissa White
You're right. Eucalyptus should be on both lists - toxic and nontoxic. According to Dr. James Harris, author of ParrotChronicles.com's Ask Dr. Harris column, eucalyptus got a bad rep years ago when it was sold as nesting material. The shredded plant invited the growth of aspergillus spores and birds died from mold infections. So it's still not a good choice for bedding, no matter what the variety, but eucalyptus should not be written off entirely. Ask your veterinarian if the eucalyptus in your area is safe to give to your bird.
--Editor
ParrotChronicles.com