I think everyone here has done a very good job to cover most of the bases, but I just have a few comments to add.
For one; yes your bird can be sick and extremely contagious without you knowing. My sister-in-laws cockatiel has a virus that causes her to self mutilate. The veterinarian told her that a lot of birds have it, but don't express it...I'll have to look up the name...As her cockatiel has lived with two of her other birds in the same cage for years, you can bet they have it too. But neither of them are expressing it.
The same sister-in-law almost lost the same bird when she took her outside years ago. While she was VERY well clipped. The little brat caught a gust of wind and flew over a fence. They found her hours later sitting on top of a pine tree, watching them scouring the neighbourhood for her.
Also, yes. Hawks can, and WILL take bids off the hand. Even trained falconry hawks. Mountsberg employees (a park in Ontario that has rescued wild birds-of-prey) absolutely HATE Harris Hawks. One trained Harris was brought to show off to visitors. It attacked and killed one of the Mountsberg American Kestrels. RIGHT off an employees glove.
And in addition; the transfer of disease can go the other way; from wild animals to your bird. I am very anal about letting my boy outside for that reason (as well as because of the risk of him flying away). If your bird encounters some bird poop, shed parasite eggs, sits on a perch where a mite-ridden bird had sat earlier, drinks from a puddle, etc. etc...you get my drift. You are not just exposing wild birds to your bird. You're exposing your bird to wild birds. And as a domestic bird, YOUR bird has no natural or earned immunity to anything you might find in the wild.
And for interests sake; have a look at this link...
http://www.bbc.co.uk/nature/life/Rose-ringed_Parakeet It is about the invasion of pet Ring-necked Parakeets in Great Britain. I think its even more scary, because Great Britain is most definitely NOT tropical. But they survive none-the-less.
