I can't find the more technical article I had about the bunnies, but this one is ok and probably easier to understand. A big enough scare floods their body with adrenaline and cortisol, and since bunnies can't escape, the stress response doesn't get alleviated, and it basically kills them over 24 hrs by causing organ failure.
Bird volume:mass is a very odd thing, as their body composition is so different to ours, as we're built to be solid, and they're built to fly. It just doesn't compute naturally based on the knowledge of human bodies. Everything internally just gets even stranger.
Being afraid of people is not always maybe the best phrasing. We don't want any of our patients to be fearful. That's going to hurt their treatment or just outright kill them from stress like the bunny babies. We do all we can to make their stay as comfortable as we can accommodate. The things we are trying to prevent are: a) babies thinking they are human, and b) adults thinking being in the presence of humans is better/safer than being out on their own.
Item A is pretty easy, and we limit access to animals in the imprinting window much more than with animals outside that window, and that's when we'll hide our faces/silhouettes/etc. We keep them with their own kind whenever possible, so all the behaviors they mimic will be proper for their species. Any animal we treat has to be legally and ethically done with the goal of release to the wild. Any unnatural behavior they learn is going to impede that, and if they imprint, they either become a lifelong adoptee, need to find a home at another licensed facility, or they get put down. None of those are often ideal, so it's something we all strive to avoid.
B can be the trickier one, though really the problem often solves itself by the fact we're usually so dang busy we don't have time to get an animal that accustomed to any of us. Each person they interact with somewhat resets them getting used to us, as they evaluate us individually. But if they feel too safe around us or humans in general and get it in their minds that staying at the clinic or around people is a better life than what they would have being independent in the wild, that's the problem. Elliott, our GHO, is a prime example. I forget if he imprinted before he came to us or after, but he failed release twice before we kept him. He would be found in people's yards looking for food, and if we as humans could catch him 2 more times after his initial capture, we are nothing compared to dogs, cats, other predators, or people with intent to harm animals that he could have encountered in sticking around yard instead of off in the woods away from us. It also gets them much closer to our cars and homes, which are major physical hazards for all types of wildlife. It makes them reliant on us for things they need to survive while also bringing them close to physical danger and predation.
So being afraid of us is somewhere between poor phrasing and oversimplification, we just want them to want to be on their own as nature intended, not wanting to even begrudgingly move in with us.