If the vet was truly educated about birds, flight and how important it is to them, s/he would not have said that.
So much more comes up all the time about how important flight is for birds - not just their physical health (musculature, their complex breathing systems, even their brain cells connect better if they get to fly), but their mental health as well.
Clipped birds much more easily become phobic and nervous and their self-confidence gets a real blow since they can't "save themselves" if they fall, they can't go where they want, they can't move around in the most natural way for a bird, and - they are prey animals. They get spooked, their instincts take over completely, and they fly for it.
Clipped, and the bird falls to the floor, possibly even breaking the beak or keel bone (the big bone birds have, covering their entire chest, where their massive flight muscles attach). No flight, no flight musculature, and a sensitive bone might break.
People say it's for their safety. But - and now, keep in mind that the intelligence and emotional maturity of a parrot equals that of a 3-5 year old child - imagine you have a toddler who's learning to walk. He falls and scrapes his knees, because he can't of course learn to walk overnight. (Just like it takes a while for a bird to learn how to turn and land properly.) You put him in a wheelchair for the rest of his life, to keep him safe.
He sure is safe - he can't run into the street and get hit by cars, he is less likely to run up to dogs and get bitten, he can't fall and break his legs, and he is overall saved from some of life's dangers.
But he is instead just made vulnerable to many other dangers, and while a human in a wheelchair can be happy, it will never be the same life as someone who has full use of their legs, especially children who wants to run, jump and climb (just as birds want to fly). In the same way, a bird that is wing clipped is severely handicapped.
Not to mention obesity from lack of exercise. Sure, he can exercise his arms in the wheelchair, but not all of his body.
"You can live 'safely' in a wheelchair for eighty years, but do you really want to?"
And the safety is really only very much what you make it. I have a Meyers parrot since eight years, and she was clipped for perhaps three years, but then I decided to let her fly and will never clip a bird again. She's fallen into the bathtub multiple times, she even fell into the toilet once - all when she was clipped. I had a flighted lovebird who drowned in the aquarium - because I wasn't there to watch her! Other than that, I had for once forgotten to cover the aquarium, and the water level was too low, so she couldn't save herself.
It was all my fault, not because she wasn't clipped.
I had an Eleonora Cockatoo who for a while felt so bad (for other reasons) that he clipped his own wings. He had never been clipped and I never planned to do it, but when he trashed his flight feathers I had to cut them, since he couldn't stretch his wings without the feathers getting tangled.
After that, he couldn't fly for months, and was depressed. As soon as just a little of his flying ability came back, just a jump from my arm to a chair - he shone up, and was HAPPY again.
And once during this time, I took him for a walk outside. I, like many other people, believed that when the birds wings are clipped, they can't fly. And sure, my cockatoo never flew inside during those months. But BANG - he got spooked, flew right up into a tall tree, then far away, HIGH up in the wide blue skies, and I didn't find him until the day after.
Clipped birds fly away all the time because their owners think that "they can't fly". The only safe way to take a bird outside is in a harness or cage.
I got him the year before as a very young and very clumsy flier. But we trained and trained and he was SO happy every time he could turn and land properly - you could just see the pride shining from him.
Flight is so imperative to the mental and physical health of birds, that wing clipping is even being banned in my country (Sweden) now. After all, birds have existed and ruled the skies for 150 000 000 years. Do we really think we can just remove what makes them birds without it having any repercussions, for the birds? (If someone sais "I clipped my bird and now everything works great!" - Ask them if they've asked their bird what it thinks.)
It is like keeping a fish out of water, a monkey from climbing trees, a horse from running.
Respect them for what they are, and don't get a bird if you can't handle and keep a flying creature safe, healthy and happy.