However, there are seemingly redundant texts in the rules that exist to either foster clarity, or to cover corner cases.
From the book?
You are bloodied when your current hit points drop to your bloodied value or lower. Your bloodied value is one-half your maximum hit points (rounded down). Certain powers and effects work only against a bloodied enemy or work better.
That's it. That's all the rules text on what bloodied is.
Dying:
When your current hit points drop to 0 or lower, you fall unconscious and are dying.
Some things to notice: Bloodied is not a condition. Dying -is- a condition. But they are not mutually exclusive. Bloodied does not mention consciousness or even 'not dying' and dying does not exclude bloodied.
So... if you have the dying condition, chances are you're also bloodied because a negative number is less than a positive number.