Heavy metal toxicity is a known issue, primarily for birds kept in poorly made cages. But this would be mainly lead and zinc. Iron is not toxic in the same way as these. In fact iron is an essential part of their diet as it is ours though this is rarely worth consideration as unless there is an underlying disease most birds, and most humans, get plenty of iron in our diets without having to fuss about it.
Can they get too much iron? Sure, in principle too much of anything can be dangerous. But again unless there is some underlying disease, or the bird is skipping meals to eat the rust off of an old cage, excess iron would not be an issue.
There are two dangers in this type of "folk medicine" - one is that the treatment needed to save a sick bird is not likely appropriate for a healthy bird: if it ain't broke don't break it. And two, often the suggested 'treatments' themselves will be deadly.
I had a coworker who recently broke her leg. She had to wear a cast to heal, and pretty quickly she was all better. This is not a reason for the rest of us to wear a cast on our leg just to make our legs stronger - that'd be a very foolish idea.
If your bird is not sick do not treat them. If your bird is sick seek the advice of a veterinarian, not an acupuncturist or homeopath (or psychopath).