I agree with you that these test are not ideal but they are a useful tool to prove that a particular DNA or RNA is present. They are specific in that only DNA or RNA sequence that matches the required code will be amplified. Others are rejected.
The real problem is that the amount of viral DNA or RNA is extremely miniscule even when it causes death. There is not enough present to easily prove its existance so that it has to be amplified.
Also, we need to remember that the bird flu does not kill humans. The body literally kills itself trying to stop it.