I think the definition of what trust is varies from parrot to parrot, depending on them as an individual as well as their past life experiences. A hand raised baby, brought into your home as a juvenile will likely warm up to you quickly and be willing to learn to enjoy petting/physical contact. An older bird who has had bad past experiences with people may never particularly desire to interact with you on that level.
One of my moms zons was wild caught as an adult bird, and even after 40 years in the same loving home, she doesn't allow petting and only steps up away from her cage. She is a very sweet and confident bird, but she will never enjoy human contact. She was, obviously, very traumatized by her experience (capture and quarantine) and she still hasn't forgotten it. She does show her affection in other ways, like playing with your hair if your sitting down, preening your toes, or fluffing up right in front of you looking soooo soft, but you can't touch her. My moms other zon and too', on the other hand, are very friendly birds who love any kind of petting/attention they can get. They will step up to just about anyone, the too' will even crawl up your shirt and pop his head out and let you hug on him! They were both hand fed babies, and one home birds. My husband an I have had our BFA for 5 years, and we are (as far as we know) his 3rd home, (he was outright neglected in his last home, and who knows about his first). He reminds me very much of my parents wild caught zon behavior wise. He is very timid around people, but also very independent. We pushed the stepping up on command, since he is not flighted and it's important he comes to us on command, but I don't push him to accept petting or physical contact if he doesn't want it. My husband pets on him, but you can see it in his eyes and body language that he doesn't like it one bit, and I doubt he ever will. I take a much more laid back approach with him that so long as he steps up and doesn't bite, that's all I ask (took about a year to train him to step up). My husband has taken a much more "you'll do as I say" approach with him. He's a lot more friendly towards me, but he listens and behaves better for my husband. Even after 5 years though, you can still see in his body language that even though he comes to us and interacts with us, he still isn't 100% trusting.