A recovered animal can't test negative while shedding active virus,because the test either checks for the virus directly (example, HIV-PCR) or antibodies made in response to it (example, HIV-Oraquick test).
I will confess to being woefully challenged to read the science but if a "recovered" bird is still shedding virus (which, apparently they can do for 4 months) (and which I take to mean that they can still contaminate another bird and/or the environment birds share) ARE they "negative" in any practical sense?