I came to this thread late, but I was going to say that Borna Virus is extremely rare, and there are usually other classic signs/symptoms besides what you describe. So good deal, great to know for sure for peace of mind.
If he was a young chicken species under a year old I'd be certain he had Marek's Disease, as those are exactly the two calssic signs/symptoms of it...but luckily parrots cannot contract Marek's.
What you're describing actually sounds more like a neurological issue to me...How old is your Green Cheek? Has he ever had any accidents like flying into anything, ceiling fan, etc.? I have seen several birds over the years who's feet curled after a head or spine injury...The "leaning back" all the time is also typical of a neurological issue, or a spinal nerve issue (the sciatic-femoral nerve typically, which will effect both the legs/feet and the spine)...
Had he had any breathing issues, like coughing, wheezing, etc.? The reason I ask is that both of the symptoms you're describing are also early signs/symptoms of Aspergilliosis, but the respiratory symptoms should start soon or have already started...
Have they tried giving him any type of NSAID yet, like Metacam, or a corticosteroid injection? Usually they'll do this early-on, because if the bird shows any signs of relief or improvement of symptoms within a week of the start of the NSAID or the corticosteroid, then you know that it's definitely due to a nerve issue or some type of compression due to inflammation...Start easy and then move-on to the harder diagnoses...The Celebrex is an interesting option to try after ruling-out Borna Virus...what are they thinking the issue may be?