It's true that a single bird will have a better attachment to you than if it's with others of its own kind. Our first few parakeets were just gotten one at a time, and they were very friendly with us. Our first one was great! He would sit with us when we watched TV, loved walking inside our cartoon glasses (we had collected Smurf drinking glasses at the time), ate with us, etc. When we got several at a time and put them in a new, bigger cage, they weren't as friendly as the single ones we'd had before them. Two were still pretty good, but the one white one we had with them (named her "Spook"; the blue one was "Sky" and the yellow one was "Sunshine") was very unfriendly. She never warmed up to us, ever.
We got all of our birds very young. The two parrots we have now are both very friendly. You have to spend a lot of time with birds and be consistent about it though. If I miss spending even a few minutes with my Quaker in the morning, she'll hold a grudge and will either refuse to come out of her cage, even into the next day, or will go into attack mode. She'll shake her toys menacingly, make lunges at me, and if I get too close, she'll bite to draw blood. The Eclectus is more forgiving, but can also get rather moody at times. He'll give warning pushes first before getting annoyed and biting when he wants to be left alone because of some upset I've seemed to cause him. Every bird is different, even amongst the same species. Some take longer to befriend than others. You just need to be patient and consistent. Some birds may never warm to a human.