Unfortunately, many vets just haven't got the knowledge to handle ailments found in birds and any non-mammalian animal. This is nothing against vets, it's just that veterinary science is so complicated that it is impossible for one person to know all about biology of all animals and their mainstream is cats and dogs.
You left out some vital info that the vet should have asked about. Do the droppings look normal or watery? Did the vet examine a scraping of dropping from the carry cage under the microscope for parasite eggs?
One of your statements is a bit worrying; bright eyed and plump.... Bright eyed is very good. Plump is a definite no-no. Most pet parrots are obese.
The reason that it resumed its ailing behaviour when you got it home is that it feels safe at home. Birds are experts at hiding an ailment to avoid being picked out by a predator.
When it is at rest, does it sit on both feet (bad sign) or does it pull one up so you can only see one foot on the perch (good sign).
Does the cere (nare, nose) show any signs of discolourment - it should be clear blue in males or brown in hens?
Does the cere show any signs of white encrustment (scaleyface, may also be on the legs) or surface irregularity?
If no better by now try to find a local budgerigar or general bird club through the council advisory or indeed on the Internet.