I'm guessing that the owner knows his bird well enough to tell if it's happy or not. Some people assumed that I was being mean to my dog when I grabbed his tail, because he would spin around and bite my wrist. But actually it was his favorite game, which he came up with, not me. He would walk backwards to me with his tail sticking out because he wanted me to grab it.

I had the same thought, in a Pixar movie this could be a tear jerker scene, in real life that bird might die of a heart attack.

I also don’t think those holes are enough to keep it from getting uncomfortably hot inside that plastic bottle. There must be another way to secure the bird without encasing it in a sauna.

Not necessarily. You are projecting your own fears in that situation onto the bird, but the bird wouldn't have the same perspective.

As a human, your brain evolved over millions of years to only feel comfortable when you are standing on solid ground. Flying through the air is about the most alien experience a human brain can have, and it won't respond well to that situation.

But a bird's brain has evolved to be extremely high and not think twice about it, probably even enjoy it. Ever see a flying bird that didn't look happy?

So while you would be naturally freaking out at flying around like that, a bird would probably feel right at home, and relaxed.